Help?

I have a 2002 Volkswagen passat 1.8 litter turbo and for about 2 months my car would only drive in 3rd and whenever I took a turn it would drop in neutral and only Rev up instead of drive and I'd have to shut it off and put it back in 3rd and it would do it very frequently every time the car was driven. So I put all together 5 quarts of tranny fluid in it and it drove for alittle longer. Then one day when taking a turn and the car dropped into neutral, it wouldn't drive again, it had to be towed back. For the past month or two it's only been able to reverse, so it's been parked and not driven. One day about 2 weeks ago the car had died and when it got jumped it actually drove in 'drive' around the block and when I reversed it and parked it and shut it off and turned it back on it wouldn't move at all, just recede up as if it were in neutral and the car died again. Reverse works fine, but the car will not drive forward whatsoever, whether it's in 'drive, 4th, 3rd or 2nd'. My boyfriends father said it may be the neutral safety switch, but I'm not sure. Everyone I've tried asking has no clue. Is there anyway someone could help me and let me know what's wrong?