remote entry doesnt work and a few other problems

hello all, new member. my key fob does not work. it wont unlock the doors or open the trunk or honk the horn. i changed the battery, i tried to resynch it. no go. also i keep getting a message that says " service stability system" and it will say "stability system active". normally this wouldnt bother me, but everytime that message comes up the car kind of swerves. AND, my fuel gauge reads full most of the time until im almost out of gas then the fuel light comes on. does anyone know which direction i should go from here with any of this? thanks

just to add to your message. I have similar symptoms on my car. 93 buick lesabre 200 000km. My trunk release does not open anymore, My cruise control stopped working, My defrost does not work and when it is pressed it will screw up the windows from working for about 5 minutes.

Everything else works though. I have a feeling it has something to do with the computer in the car but I have never gotten any codes that say it is the computer.

The fuses are still good.

Anyhow I figure if you find out what is wrong with yours it might also cure mine.