looking for some help, my 97 850 t-5 runs great for 2-3 hours and then when ever i come to a stop or a stop light, the idle becomes rough and drops below 500rpm's, as soon as i take my foot off the brake and hit the accelerator the car hesitates and than stalls and i coast to a stop and have to restart it, i had to drive with one foot on the brake and one on the gas to keep the revs high too many times now, i had the fuel pump relay replaced due to cracks, and it seems as if the problem was gone but it reared its ugly head once again but while i was driving at like 75 mph i almost became a road waffle, when its cold and i dont drive the car for more than 2 hours i have no problems but if i have to drive for longer than 2 hours this problems always happens, i have taken it to my mechanic and he was stumped i also took it to the volvo dealership but they really didnt take much time to look at it because they wouldnt drive it for more than 10 mins to try and reproduce the problem so no problem occurs so no attempt to fix it, so now im lost and have no idea where to turn, my car ran great the first 3 days i had it then this crap happens, when its cold runs fine once the engine temp gets to what i would say optimal range it starts acting up, any advice would be appreciated, also there is a loud buzzing noise by the battery behind the front headlight i have no idea what that is either, but im more worried about stalling than that noise im hearing, again any advice would help -Thanks

There is an air pump under the battery, but that is only supposed to run for a couple of minutes after cold start.
Your engine should warm up to normal within 5 minutes of driving, even when the temp is below 0F. If it takes 30 minutes to warm up, get a new OEM thermostat.
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My name is Klaus and I am a Volvoholic.

so will the thermostat stop the stalling?

No, but if the thermostat is stuck open (the default for an OEM) then the engine will run cooler and richer than it should, causing the spark plugs to foul.
Eventhough your post was long, there were few specifics that will pinpoint where the real problem lies. If there is no check engine light, that usually points to a fuel delivery problem or a bad vacuum leak.
Just for fun, stop at a local auto parts store and borrow a scanner. If there are any codes, including "pending" codes, let us know.

One of the brickboarders had some jelly like goo in his tank a while back. After running for a while the goo covered his fuel pickup filter and slowed the flow of fuel. No codes. No idle problems. And, until he pulled out his pump, no engine problems. It did require pulling out the pump and looking around with a flash light.

All I am saying, we need more input to solve your problem.
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My name is Klaus and I am a Volvoholic.

removing what pump ? the fuel pump?

I just related a short story that was told here. I find it hard to help without more data.
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My name is Klaus and I am a Volvoholic.