I think what has happened is that your computer loses all power when shut down. This means that everything on your hard drive and not hard written is erased, and usually the clock runs off of a small battery that recharges when your computer is on.
I don't know what system you have, but chances are, your battery is either disconnected or toast. This dead battery would cause you to lose your clock data, and computers cannot run without a clock. (This is because for data to be used between computers, they must be synchronized. The time need not be correct, but the time must be entered)
I assume you have a PC, not a laptop. Open up your tower and check for a little Cell battery. Mine is right behind the front fan. But yours could be anywhere.
You can't replace it. The only way to do that is either jerryrig it, which is unsafe, unreliable, and could cause a fire, or you could take it in to a repair place.