I agree, it's probably a hardware problem, but if it's fixable we may as well save you that $300. 😉
Do you have much free space on your hard drive? If you have more than 10 GB free, boot to the installer again, and follow these steps. It shouldn't affect your files or user profile or anything that you're currently running, but it will help to determine if the problem is hardware- or software-based.
1. Once in the installer, go to Utilities -> Disk Utility, select your iMac's hard drive in the left-hand side (the one that's not indented), and go to the Partition page. Click on the main partition in the list (named Macintosh HD by default) and click the + icon at the bottom of the list. Set the size to 10 GB, then click Apply. Close Disk Utility.
2. Go through the installer, and when prompted tell it to do a new install to the partition you just created in step 1.
3. Towards the end of the instal process, you will be given the option to customize. Deselect everything that can be deselected, then click Install.
4. Go get yourself a cup of tea while the install process goes.
5. Once the installer reboots, you will be asked to configure the computer. Go through that until it asks you for registration information, then press command+Q so you don't have to bother with that again. (You probably already did it when you first set up your computer.)
6. Eventually, you'll make your way to the desktop of your fresh OS X install. Plug in your flash drive again and see if it works.
You'll be able to delete this partition later on and reclaim that lost hard drive space. Just keep it for testing for the time being.