Q: a blue screen appears after a gray screen with the logo and the spinning gear

Try using Disk Utility to do a Disk Repair, as shown in this link, while booted up on your install disk. You could have some directory corruption. Let us know what errors Disk Repair reports and if DU was able to repair them. This could just be a start in repairs and you may need a better utility to finish the job.

Then Repair Permissions.

No need to report any Permissions errors........we all get them.

   DALE