Could be what is called a "short start" syndrome which is common to that year rotary. My 86 RX7 does it every time if I am not careful. Hmmmm....crazy rotaries. Anyway, being that yours has sat for so long and it's cold out all bets are off. However, here's a little info and what to do if you are interested. I just copied this from another site. Kinda long...
Common Symptoms
Vehicle was running fine the last time I parked it, but now it won't start
I can hear the engine rotating, but it sounds strange. Also, I smell gasoline.
I moved my car from the garage to the street, turned it off and now it won't start.
I left my car with a friend and they moved it. Now it won't start.
My car has been sitting for a long time and won't start.
Background
The RX-7 (especially 1986 and newer) is well known for flooding problems. One of the most common is caused by a "short start" condition. The "short start" is when someone starts the vehicle and turns it off before it is allowed to reach full operating temperature. The typical situation is moving the vehicle from one parking spot to another(ex: from garage to driveway). Cooler weather, especially temperatures below 70 degrees, aggravate the situation. What has happened, is the engine is still in the cold-start warmup cycle. Due to a fluke in the engine management's fuel injection computer, if the engine is shut off during this cycle, it is highly likely the engine will flood itself out the next time the engine is cranked. It does not matter whether you wait one hour or one week, the computer will wait for you the next time it's started. Once again, this is not something that will present itself as a problem every time you short-start the car. Of certainty, the problem will not occur if the short-start situation is always avoided and the vehicle is in proper mechanical condition. If consistent starting problems are experienced outside of the short-start situation, service is probably needed to the vehicle.
Rules of thumb
You will have to actively unflood the vehicle. RX-7's WILL NOT unflood themselves, even if allowed to sit for long periods of time.
DO NOT pump the gas pedal at any time while cranking the engine.
If the vehicle doesn't start within 5 seconds of cranking it's probably not going to start without unflooding.
If car is heavily flooded, spark plug replacement and oil changing may be required.
There is no cure for the short start problem other than the discipline to avoid the situation
ALWAYS ALLOW THE VEHICLE TO REACH FULL OPERATING TEMPERATURE BEFORE TURNING ENGINE OFF
Easy 3-Step method(1986-91)
PREPARATION
Battery needs to still have a reasonable charge. If engine is cranking slowly, please charge battery first or connect jumper cables.
STEP ONE
Locate main fuse box next to battery under the hood.
Pull innermost fuse from fuse box and leave out. Lid will have fuse labeled as "EGI Comp" for 1986-88 models and just "EGI" for 89-91 models. Note: some models have empty spaces for options on vehicle. There will be no fuses in these spots.
STEP TWO
Once fuse is pulled and left out, get back inside vehicle. Hold accelerator pedal to the floor and crank for 15~20 seconds. Vehicle will not start during this procedure. Remember, it is key to this procedure that you hold the accelerator down and crank the engine at the same time.
STEP THREE
Turn ignition off and go back to the main fuse box. Place innermost fuse back in place and get back in vehicle. Try to start vehicle like normal WITHOUT touching the accelerator at all. If vehicle doe not start within FIVE SECONDS, it’s not going to start without doing the "three-step" method again. Sometimes this procedure has to be done five or six times to get vehicle started. If vehicle still won’t start, make sure battery is charged adequately or proceed to complex process, if your mechanical abilities allow.
Note: Vehicle will smoke heavily for awhile after startup. The more flooded the engine, the longer it will smoke.
Complex Unflooding Procedure(86-91)
Note: This procedure is only to be done by persons with adequate tools and experience. Also, it is intended to be done after attempts to unflood with the Easy 3-step Method have failed.
TOOLS
Standard 13/16 spark plug socket and ratchet
One quart automatic transmission fluid(ATF)-any type
Oil squirter, fluid bulb(like a baster), or funnel with hose
NGK spark plug set(if needed)
PREPARATION
Battery needs to still have a reasonable charge. If engine is cranking slowly, please charge battery first or connect jumper cables.
STEP ONE
Locate main fuse box next to battery under the hood.
Pull innermost fuse from fuse box and leave out. Lid will have fuse labeled as "EGI Comp" for 1986-88 models and just "EGI" for 89-91 models. Note: some models have empty spaces for options on vehicle. There will be no fuses in these spots.
STEP TWO
Engine has (4)spark plugs arranged in a square pattern on the drivers side of engine. Please label each plug wire and remove all four plugs. Note: It is absolutely imperative that the wires be able to go back onto the correct spark plug hole when the procedure is completed. Also, make sure plug wires are out of the way of the accessory belts to avoid tangling when engine cranked in step three.
STEP THREE
Make sure all spark plugs are out of engine, EGI fuse pulled, and plug wires out of way of accessories and belts. Get back in vehicle, hold accelerator on floor and crank for 15~20 seconds. It is very important that the accelerator be held to floor during this process. Note: You will see lots of gasoline vapor misting in engine compartment. This is normal and will diminish during cranking process. Engine obviously will not start at this time.
STEP FOUR
Place approximately one ounce of automatic transmission fluid(ATF) into each of the bottom two spark plug holes. This will be difficult, but ABSOLUTELY necessary. The fluid will relubricate the chambers of the engine and allow it to build compression. Use any type ATF and any reasonable means to get fluid into engine.
Examine original spark plugs. Clean and dry carefully, if still in acceptable condition. Use a brand new set of NGK plugs, if necessary.
Install plugs and reattach spark plug wires. Note: As mentioned before, it is absolutely imperative that the right wire go to the right hole. Wires can be traced one-by-one from their coil connection. Each coil connection has labeled L1, L2, T1 or T2. Remember T stands for top, L for lower, 1 for front and 2 for rear. Also remember, there are different plugs for the top and bottom plugs. The ones with the blue banding at the insulator tip are the top two.
STEP FIVE
Place innermost fuse back in place at the main fuse box. Get back in vehicle and try to start vehicle like normal WITHOUT touching the accelerator at all. Engine should start almost immediately. On rare occasions, this procedure has to be repeated.
Note: Vehicle will smoke EXTREMELY heavily for awhile after startup. The more flooded the engine, the longer it will smoke.
Once engine has warmed up completely and battery has had some time to charge, turn engine off and restart. Engine should start normally. It is highly recommended to change the oil as soon as possible. Oil becomes heavily gasoline contaminated from the flooding.