Is there any reason for the boot order to be different from what it was before?
A) Was the shutdown "as usual", or was something not expected? What I mean is, did you actually shut down the system, or "something" made the computer shutdown "by itself"?
B) Is a "desktop" system? If the computer has batteries, plug in the power cord and leave it connected until all the checks/test are done, in case the problem is somehow related to the batteries.
C) Can you report the exact model(s) of the hard drive(s)?
D) Can you get to the BIOS? Is the BIOS detecting the hard drive(s)? Is the information in the BIOS correct? Is the BIOS detecting the hard drive(s) correctly?
E) Can you boot the computer with UBCD, or with some boot CD or bootable usb, instead of booting to the hard drive?
If you can report back your test/info for the above checks, then maybe we could find if the problem is related to software or hardware, and then, according to the info you provide, we could maybe suggest what tool to use.
Try to find the answers for the above questions and report back whatever info you can.
In addition to the above questions:
F) I wouldn't discard so fast a virus problem. I'm not saying it "has" to be a virus, and I can't say that the game you installed has a virus for sure. It could be a coincidence, or not. I'm just saying, after reporting back the previous questions, it would be very advisable to run a complete check with some UPDATED antivirus rescue disk (that boots from CD/DVD/usb) and can completely check the system, including BIOS, the whole boot process sectors, and the whole hard disk.
Report back and we'll continue from that point accordingly.