What happened?

Do you have an installer DVD for the machine? If you do then see if you can boot from it without the same thing happening.

If you have a machine with Lion or Mountain Lion pre-installed then try booting from the Recovery HD.

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

And, what version of OS X is installed?

Finding your Mac OS X version and build information

If you never upgraded it, then most likely it came with Snow Leopard. Two years ago makes it a 2010 model, I'm guessing. In that case you should have received a set of two DVDs. One would have been the OS installer disc. The other contained the bundled iLife applications. Best Buy must have sold you a demo or floor model on sale but didn't give you the discs for it. They owe you those discs. Otherwise, you will have to purchase replacements from Apple - Contacting Apple for support and service - this includes international calling numbers.

Meanwhile you can take the computer to Best Buy for repair because without the installer disc there isn't a whole log you can do. Do you happen to have a recent functioning backup?

Well, that would make it a 2010 model, so if you haven't upgraded, then you would be running Snow Leopard - 10.6.3 or 10.6.4. Naturally, they will say it's the motherboard without testing in order to prepare you for the worst case scenario.

The first thing to do is take it in because you don't have an installer disc. Be sure they first try booting it from an installer disc. If it does the same thing, then there's a hardware malfunction. I assume you did not buy the extended warranty, so if it is a motherboard replacement, then be prepared for a hefty repair bill.

If you still have your original box then you may still have the install discs and not even realize it. The install discs are stuffed behind the tiny little 5" X 5" 'Everything Mac' user guide that is dropped into the cutout on the top of the foam block that you had to remove. Unless you are specifically looking for the discs they can be easy to miss.

Here's an article that may be helpful, although you really need either a bootable external hard drive or install DVD to troubleshoot further. Disconnecting all attached peripherals besides the keyboard and mouse is also a good idea in case one of them is causing the issue.

http://support.apple.com/kb/TS2570

Having a wireless mouse and keyboard should not cause any issues of the type you are experiencing. I do suggest temporarily disconnecting any other devices you have attached just long enough to rule out whether they are contributing to the issue.

If you locate the install discs in the box then you can attempt to boot from the install disc by powering on the system, then immediately hold down the option key to bring up a list of bootable devices. The install DVD should appear. Another option is to hold down the 'C' key which will attempt to boot directly from the optical drive instead of bringing up a list of bootable devices.

http://support.apple.com/kb/HT1533