I agree with ruffrider285, change the fuel filter first. It's a good thing to do anyway... just have lots of rags on hand to soak up the extra fuel.
Jack up the back of the car, the fuel filter is a round can in front of the rear axle. It's got a quick-disconnect fitting on one end (green clip comes out first) then the threaded end. The threaded end is usually a pain in the butt if nice and rusty, as they usually are after 5 or more years. Soak it in PB Blaster or another rust penetrant for a while before you try and crack it free. Use the right open-end box wrench on it... not an adjustable one, you WILL strip it out.... then you need to cut and splice lines which is not fun. When you take the filter out, drain it into a clear mason jar so you can see how dirty the filter was... it will probably drain out nice and black
Oh, and go to a GM dealer and buy an OEM Delco fuel filter. Don't use the Fram garbage. Trust me
When diagnosing the fuel pump... when you first turn the key to ON (but not start), you should be able to hear the pump "prime" for 3 seconds or so and shut off. If you're not hearing that... then the pump is dead. These pumps don't come back from the dead... so if you're able to start it after a while, that's probably not the issue.
Oh, and BTW... there are no access panels on Cavaliers.... at least, not the third gen (95-05). Only the larger GM cars have an access panel. You do have to drop the tank... and it's a pain if there's more than a little fuel in it. It has to come out at an angle.... and the whole fuel assembly with sender and float are one component... you can't easily change JUST the pump. Unless you want to do a little upgrading for a high hp application, and are swapping the fuel pump itself for a Blazer or other high-flow pump... but that's beyond the scope of this post
Two more things to check... because I've had this happen to me too.... the fuse in the dash panel, and the relay under the hood. Check them both for corrosion on the terminals. Clean 'em up with a little steel wool and you might fix it
One more thing I forgot.... there's a recall in some areas for the level sender... it reads 1/4 tank when it's really at empty... some fuel additives can corrode the silver terminals on the level sender. I died on the highway with 1/4 tank... not good! I know it's a recall in BC and Ontario... not sure where else. A good reason not to use ANY fuel additives!!