I'm almost certain it's the starter. Sounds exactly like what happened to my '94 LS over the past couple of weeks. When it started, it would run fine. The problem was getting it started. Anyway, I don't have any experience replacing starters, so I took mine to a local shop. Total cost was $201 and change. If you're the DIY-type, some of the prices I've found online range from $165-225 for rebuilt starters. Good luck.