Just picked up a 95 eagle talon tsi with 110,000 miles , drove it yesterday perfectly fine and today when I started up the car, it cranks over but wont start ,but if I wait for a couple minutes the car will crank over and start no problem,kinda of a weird problem ,but let me know if you guys know what it can be,thanks

I would check the plugs for the coldstart switch make sure all of that is connected
Check how old the spark plug wires are

Check that your coolant temp sensor is reading correct, and check the wiring I had similar issues when mine wasn't, if I stalled out(which was easy to do with a lightweight flywheel, a puck clutch, and dumping way too much fuel because my ECU thought the engine was 40* colder than it was, let alone when on a cold start it thought it was 40* colder than ambient air temp....) It wouldn't start up again for like 10-15m because it was flooding. Couldn't figure it out for the life of me until I had the car idling for a bit and noticed my temp gauge start reading high but my fans weren't kicking on, and my gauge had always been accurate, so I check the CTS reading and its 40* low...
I had replaced it because the wires snapped off right at the base of the sensor, but every parts store had the wrong plug connector, I tried 1g, 2g, Talon, eclipse, etc. every single variation and store had a different sensor connector....so I gave in, and bought that one and a plug tail to go with it....I wound up jerry rigging the original sensor.