96 Neon sohc intermittant no start

my daughters 96 Neon was blowing fuel pump fuse ocassionally and now it doesn't want to start every time. It will crank no problem but there doesnt seem to be any fuel pressure. You can't hear the pump with the key on when this happens. Usually after 2 or 3 try's it does start up and run fine, but it does take a few minutes. Damp or humid days seem to be worse. Is there any known problems with the fuse box under the hood that could cause this? Also the horn fuse blows constantly . I have changed the horn and the relay with no luck.
I think there may be a short in the fuse box. Any help would be appreciated.

Check your grounds or for loose/exposed wires. Fuses continuing to blow, usually indicates a bad ground or faulty wiring. Check the wiring under the battery box. Sometimes battery acid will leak out and corrode the wires.