Well the starer itself doesn't have a fuse, so it must be the starter relay.
This sounds like a relay or a wiring problem. You'll need to get a wiring diagram from the public library or the Internet (sometimes car stereo shops will sell you one for a few bucks) and figure out where to look.
The engine compartment relays are located in the Power Distribution Center (PDC) next to the battery. The PDC contains the starter relay, radiator fan relay, A/C compressor clutch relay, auto shutdown relay, wiper relay, back-up lamp relay, transaxle control relay, fuel pump relay and several fuses.