If it's cranking alright, alternator shouldn't be keeping it from starting.
I assume when you said intertia switch is fine that you mean that the fuel pump interia cutoff in the trunk is fine. When you turn it to run, do you hear the fuel pump kick on momentarily?
96 GT - Triple Black, Lowered - Full PI Swap, P&P Heads, Off-Road H-Pipe, Flowmasters
Current Project: 86 GT Hatch