KITTYFRESH2

So heres the deal purchased this car for cheap was a theft recovery they jacked the rims, radio and interior (seats, door panels, ect.) dash was all intact..

punched the colomn to hotwire it when it was stolen but you could still start it with what ever you wanted knife, screwdriver, house key pretty much anything.. the engine was untouched and runs perfect fired up everytime runs super smooth, no engine lights or anything..

In the last few months I've been piecing missing part together driving it to work and back.. In the last month the speedometer would jump around I'd be cruising at 50mph then all of a sun it would jump from 50-100-0 back/forth... after a long drive it seemed to opperate normally and work fine.. But last week it started doing it a lot more when i would start the car the needle would jump up to 40 then back to 0 and bounce from 0-10... I drove it to work about a 20min drive to pick up some stuff when i returned to leave I turn the key and it fires up then dies... I figured out te ignition was finally busted the key would not stay in the on position so as soon as you turn and the engine fired and let go the key would fall back to the 1/2 way positions so it would die.. Thinkng the key was only turned 1/2 way...

After i noticed this I picked up a new igntion switch and replaced it.. It will start now but if the alarm it set and you come back about 10mins later to start it the engine will die out after it starts..the speedometer also jumps not as much 5mph so say your driving 40 it will go from 40 to 45.. and i get this beeping noise after i turn off the engine comng from inside the car..

I took the car to have the engine tested and they say everything is working perfect
any ideas I dont want to take it anywhere far and have to get it towed back to my house..