This strange issue has been happening to me recently. I notice that when I shut down my computer, and then start it up the next time, the time and date of my computer remains the same as that of the time and date that I shut down my computer, and it continues from that time and date until I adjust it manually myself.

For example, if I shut down my computer on 3 May 2008, 10pm, even when I switch on my computer on 4 May 2008 9am, the date and time shows 3 May 2008, 10 pm.
I don't understand why, I did not automatically synchronize it with an internet server, and I've got the time zone correct. It has only started happening a couple of weeks ago.

Is there a battery that needs changing?

Something then must be wrong with the synchronization or something is screwed up with your pc. I remember this used to happen to my dads laptop, I can't remember if we did a OS reinstall or not but it is working fine right now. Did you play with a system setting? That could be the problem.

I don't think so... It's a new computer. I've only had it for about a few months.

I don't think I toggled with any settings. I don't make it a habit to do stuff like that since I know I won't be able to fix it if anything goes wrong. I might have done it unintentionally, but at the moment I can't think of anything I could have done to cause it to exhibit such strange behavior.

Hmmm....since it is new and you don't think you played with anything, all I can suggest at this moment is too backup your data and do a system restore or don't turn your computer off I suggest the first one though

The system clock, while turned off, is maintained by the CMOS battery on the motherboard. They usually last for a quite a few years, but it could be that the battery has gone flat. It's just an ordinary watch battery (those 1.5V flat disc batteries) so should be quite easy to find. Replace it and see if it helps.

I agree with rvalkass, most of the time its the CMOS battery going dead that causes this kinda problem. Honestly speaking, I just changed my PC's CMOS battery yesterday (it's been nagging me, but I just couldn't take time out for it specially). Hope that helped.