98 Explorer....many faults

in the last few weeks, my 98 explorer sport has had the following

1. The FUEL DOOR light stays on all the time, but is less visable when I turn the headlights on.

2. Now my check engine light has come on.

3. once or twice a week, the ABS light comes on for a few miles then goes out.

4. When I turn my heater on, the thermostat shoots down to cold and gradually climbs back upto operating temp, on very short journeys it does this over and over again (I changed out the thermostat last October).

I have put new battery connections on and replaced the battery in Jan, so I know that is good. Anyone out there have any similar problems?

I also need car inspection done, will it fail if the check engine light and fuel door light are both on?

Thanks.

to quickly answer your last question - In Calif. if the check engine light is on - you fail the emisions test. I suggest you buy/borrow a checker and read out any codes that may be present. it might give you a starting point. Also for the intermittant problem with lights ie, fuel door, check engine, abs .... see if you can find the computer in your car, you might be having a computer problem or a wire that is shorting out near it. I believe it is under the dash near the radio.

Double check your battery connections especially the chassis ground. A loose connection can play havoc with your computers.