97 Jetta Shuts off

97 Jetta GT. 121K miles. I was driving the car and decided to park. When I tried to turn the car on, the dash lights flashed and the car alarm weakly sounded. The dash time and stereo turned off and on when I tried to start it. Also the radiator fan would turn on and off. I took the car in and the mechanic checked and replaced the battery and it worked for a while but then kept turning off on me. It eventually left me on the street and had to have the tow truck jump start me. I drove it back to the shop and they then said it was the throttle body, catalytic converter, plugs and wires, rotor cap, and I should get this done. So I said how much they quoted 600 bucks minus the throttle body. Didn't get the work done since it seems a little hoaky. The car starts but seems to idle low when coming to a stop, and as long as I dont turn on to many items like AC and stereo the car will not turn off. Any ideas??? The alternator is good.

REplace the ignition switch electrical portion