Is my fuel pump gone out?

nope, has nothing to do with fuel pump. here is why.. when you turn your key from the column and go to the on circuit ( do it very slow) you can hear the hmmmm from you gas pump, right?? pretty good indication it's working properly. if you cannot, work the 2 man system and have someone turn key on for you while you go back to gas tank and listen for it. It has to get juice from electrical to work, right? So, car starts and drives but just dies because your relay switch is old or tired and needs to be replaced. I had same problem with my Mercedes before I realized what was going on. Relay is in fuse box about 1x1 in size look like a small black box for tooth picks. good luck