Before ruling the main fuel pump, change the fuel pressure regulator. It's the silver can at the bottom of the fuel rail with a vacuum hose attached on one end and a fuel line on the other.

A failure here causes the main pump to overchurn, hence the noise. Occasionally, the engine will just die too with no reason.

-- Kane
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Blossom II - '91 745Ti/M46 ... Bubbles - '74 144GL/BW35 ... Buttercup - '86 245GL/AW70 ... The Wayback Machine - '64 P220/M40

I had the same experience about 5 months ago on my '86. It had the same whining main fuel pump sound. My mechanic said those main pumps are very resilient - so if yours is whining it probably has the same problem as my car had - crud in the fuel tank. My main fuel pump almost went out - the whining sound is called "cavitation" which is fuel starvation. The rough running is probably from foam instead of liquid fuel being supplied to the injectors. My mechanic replaced the fuel tank with a known good used tank (he says that the 240 series tanks are very prone to rusting and almost no amount of cleaning will help a rusty tank, he has to go through 10 used tanks to find 1 good one). The crud plugs the filters and starves the pumps. The in-tank pump will go first, then the main pump. The only way to tell is to pull the main pump and filter and pour the gas out and see if it is rusty. My mechanic put new filters, a good used tank, and a good used main fuel pump on for $280.00. The car has ran fine every since then.

Hope this helps,
Lance

I would check the simple stuff first and work your way down.

Make sure your rotor and/or cap are working good...this is simple and inexpensive, and 9 times out of 10 will solve many problems with wild and crazy fuel/electrical issues. I had a GL once that was all over the map when it came to fuel starving and it would buck when I hit the gas pedal, once I replaced the cap and rotor the problem went a way and the car ran a lot smoother as a whole. Check the fuses to your fuel pumps next, simply remove the panel and twist all fueses and look for obvious broken ones. Then move on to your fuel pump relays, fuel filters, and the like.

It sounds to me like you could have a rotor/cap on the way out, a glogged fuel filter, or the highly possible rotted delivery hose on the pre-pump as rhaire suggested. But keep it simple at first...then move to the harder stuff.
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VOLVO LOVER WITH AN 80 AND AN 82

First of all the symptoms you can get from the fuel pump relay are widely variable and include something like that intermittent poor running, for sure, BTDT. Then too if someone used poor hose and stuck it on your new in-tank, that might be it. It swells and fits poorly, loosens and there you have the split hose syndrome even with "new hose". In the latter case there should be no problems at full tank and it will appear at half or so.
Do not assume the main pump is bad until you rule those two very common problems out.