As far as grounds go, not only clean them, but get a tube of dielectric grease from an auto parts store and put some of that on the connection to help prevent further corrosion.
As far as not getting any response from the computer, check the fuse for the cigarette lighter, when that fuse pops in a lot of vehicles, you get no response plugging in a code reader.
If the fuel pump is not turning on, I'd trace that before worrying about the computer. Check the fuses and relay, check the inertia switch up under the dash on the passenger side floor (near the transmission hump). You can check for power there using a test light or meter (that will tell you if all the wiring and all is good for that part of the system), then check to see if you get power at the pump. When the key is turned to the on position (not start, but run), it will give power to the pump for a few seconds. When checking for power at various spots, you may need an assistant to cycle the key.