Screwy Volkswagon

I have a 00 Volkswagon Passat turbo, manual, with 83000 miles. This car was sold to us as 'salvaged title' and we have already had the engine replaced once due to four holes in the engine block from faulty hoses, pressure, etc. That was done a little over three months ago. Now there is another problem. Well, two. The check engine light comes on whenever you get to third gear and accelerate to get into fourth. The mechanic said I need some kind of plug replaced. [Just saying this incase this is connected somehow to my real problem.] The real problem is that my car will not start. There is no ticking sound, it will not even turn. When I go to start it, it makes this really loud buzzing noise from the dash area. When it first happened, I tried it about 3-4 times, and it started and ran fine. It sat for about an hour, drove it again, started no problem. About two hours later, went to start it, it wouldnt start for the world. Kept buzzing. I would take my foot off the clutch and it would stop buzzing. A few mechanics came over to look at it, jumped it and it started. Pushed it out into second gear and it quit working. Every time the mechanic has gone to work on it, it keeps starting so they "cant" find whats wrong with it to fix it. I took my car to autozone and had a battery test done and its only two years old. The guy says it reads just fine. The mechanics said they checked everything with the alternator, starter, etc to see if any bad connections were there. Its been there for over a week now and it starts every time. I dont want to pick it up and get stranded somewhere. Any ideas?