2003 Jetta Wagon 1.8T Electrical problem

When driving sometimes I will hear 3 long beeps, then shortly after (usually at a stoplight or when accelerating from a stop) the entire engine will either shut off and all the lights will come on on the dash, or it will "reset" and the warning sign with an arrow around it will illuminate for about 3 seconds. The car ran fine after we got it used in 2005. It ran for 6 months with no issues. Then it got broken into and the safelite guy who replaced the glass let the battery run out. He said that he tried to jump the battery but couldn't get the car to start. We got it towed to a repair place and they put in a new battery. Ever since we have had nothing but problems. We took it to the dealer and they said they ran a 27-point inspection and cleaned the throttle body ($200). That didnt' work so then they said the vacuum hoses were cracked and needed to be repaired ($300). Then we tried a Volkswagon repair shop instead and they said that they had to clean corrosion from the battery terminals and fusebox($150). No luck. Then they said it was a bad alternator($600 and didnt' get to keep the original alternator). That was still not it so I let the guy keep it and drive it around and he said that he was going through each and every circuit. The bill is up to $120 again and still no idea. I'm scared to just let the bill run up anymore. I can't even find out what the beep codes mean. Help.