Picture of a little engine or something that says "check" is on. why? I just bought it today!!

Air Bag light !

before you take it to the shop go to an auto parts store and they will scan it for free and tell you the problem

Compression check may tell you something.

Sounds like the last car I bought with"no problems!"
Start with a charged battery and clean all corrosion off cable connections before installing and tightening. Check your battery ground for a clean tight connection.
O.K., key on...still no check engine light/airbag light? You sure it's the bulbs out and not something disconnected? Try starting it. Does it crank over normally? If nothing, you mayhave a fuse out or something wrong in the power distribution center in the engine compartment. Check your fuses.There may be another center or box, too, with fuses, besides the one. Post back if you need more help. Cheers.

Since you bought it, what has been done in the way of
preventative maintenance

I would have layed it up for two weeks, and gone through the
entire vehicle,changing all fluids,spark plugs,checked fuel
pressure and on and on.

You probably bought a vehicle that is 5 or more years old,
that other than,oil changes, is the same as when it came off the
train and car hauler, on the way to a dealer

That won't work on todays high tech vehicles

Snow and cold, has little to do with todays electronic wonders

You do realize, your asking a question, when as I said, we have no vehicle
history

I don't think you understand the technology,not anyone can work on todays
vehicles. You need a 2 or 4 year college degree, if your just starting out

I will help you when you give me something technical to work with

You either have a thermostat or water pump problem. car is getting hot. Check to make sure you have no water leaks on the hoses or radiator. to check the thermostat,run the engine for awhile to get it hot and touch the upper radiator hose to see if it is hot . If so then the thermostat is working and the problem would be the water pump. hope this will help you.

The check engine lightwill turn on when the engine and/or transmission control module finds a concern. The sellers may have had the light turned off just before they sold this vehicle, knowing there was a problem. No, it doesn't monitor timing belts, or leaks in the engine, but will turn on if there is an evap leak in the purge system. Autozone usually scans check engine lights for free.

check the gear box oil or the sensor

If the starter is getting proper voltage at main lead and trigger wire (with the key in "start") pull the starter. If it was making strange sounds likely there is something wrong with it. Check flywheel as well and make sure you can turn the engine by hand. If you aren't getting the proper voltage, check the battery, connections and starter relay (in power distribution center)

UNLESS YOU HAVE WARRANTY LEFT,IT'S UP TO YOU FOR REPAIR COST..THE WIRELESS CONTROL MODULE THAT CHECKS FOR THE PROPER KEY SIGNAL MAY HAVE FAILED OR YOUR KEY TRANSPONDER MAY BE DEFECTIVE..ANYTHING ELECTRONIC TODAY IS EXPENSIVE TO REPAIR