Get a pump for sure. Check the resistance in the wiring harness, too. That's a PITA to do, but you could have a wiring problem that could cause this as well. Especially if you change out the pump and it still does it. If you search DSM forums, you will find information about how to rewire your fuel pump directly to the battery with a relay, eliminating the 40 or so feet of spliced and respliced wires that run your pump. You can use thicker gauge wire, too. It's good for a few PSI, so that's why DSMers do it, but if yours is broken, it's worth a read. check these sites...

www.vfaq.com < this site is starting to fall apart because it's been up since '95 or so... many of the VFAQ's were hosted on college campus servers that are no longer up and running so I can't guarantee you'll find it here anymore.

www.plymouthlaser.com < this guy sold his last DSM, but was nice enough to keep the site around. Go there while you still can. He's got a bunch of great turbo hacks.