I got a few problems with this car.
I had a cheap cellphone charger in the cig lighter and it shorted out my stereo.
I changed the fuses but after that it started acting up.

#1 the car will turn over, but then eventually the car will just stop.
Almost sounds like the car isn't getting enough fuel or something.

When I try and restart it, it takes forever to turn over then it eventually drains the battery.

#2 The door chime constantly goes off like the door is open and won't stop.

#3 Whenever I go over neutral, I hear a grinding sound under the hood.

 

Try the usual tune-up procedures: new spark plugs, plug wires, rotor and cap, air filter. I hesitate to say fuel filter, because that is a bitch of a job if it's under the car. If the car stays dead, go to www.stepbystepvolvo.com for free guide to 740 no-starts (B230, LH2.2).

 

It has to be something electrical, which are always fun to diagnose. I would check the fuel pump relay and also go through all the other fuses to make sure that they are all ok.

It could also me a sensor like the RPM sensor.

Good Luck.

 

I've checked the Fuses, all of them are fine.

Fuel Filter is underneath the car, my neighbor says he thinks thats the culprit.

IT does sound electrical, but I can't figure out what though.

The car is older and not worth spending anything over $300 to fix.

I will change the sparkplugs today and get that fuel filter out.
I'll see what happens then. thanks for your suggestions.