'88 735i - seems to be fuel-starved

After recently filling up the fuel tank on my 1988 735i, it stalled out on me. Now, the only way it will start is by pumping the accelerator several times- it runs normally for a few seconds, and then it idles down lower and lower until it quits. Trying to accelerate at all kills the engine. Any ideas?

Also, is there more than one fuel filter to check? I have found references to a fuel filter "near the fuel pump" that requires wrenches (10 and 17mm) to remove. I know about the one connected to the fuel lines by regular hose clamps...