01 issues

So after unsucessfully searching around this site i have came to the conclusion to just ask. I have a 01 Cobra and the other morning i went out to go to work and the key fob wasnt working. I unlocked it manually and started the car, the car starts and drives fine, but it is constantly beeping while i'm driving similar to the beep as if a door was open. The door and trunk and everything else are all closed. Also while the car is running it is trying to lock and unlock itself, you can hear it trying, but the locks are not working and neither is the switch inside on the doors. The car also beeps when the key is out of the ignition, the same beep as if a door were open. I disconnected both battery cables and let it sit for a few hours ( i know it only takes twenty minutes) and then i came home and reconnected them hoping it would fix the problem and low and behold it didnt. It also does this with my other factory key and key fob. Kinda weird... any advice would be greatly appreciated. Thanks.

Thanks for the reply, i appreciate. I'm going to check the grounds and review the attachments. As far as everything else, i have had no stereo work, there have been no accidents or wrecks ever, the only thing that has been done recently is an oil change and i had to replace the bracket that holds the fog light. About six months ago the car wouldnt start and i discovered that the posts on the battery cables were faulty. Other than that i have never had any issues and i bought the car brand new. I'll look and and try this out tomorrow and post my results. Thanks a lot, i appreciate it.