I would definitely check connections. When I first got my car I had starting issues where it would just click once. Being the smart guy I am I replaced the starter and battery to no avail, ended up being that my negative battery cable had about 3 copper wires in it and wasn't making a good enough ground. Fixed that and it started right up.
Sold - Black 2000 Mustang GT, gone but definitely not forgotten
- Silver 2007 Corvette
Current - DHG 2001 Bullitt