PC Boots to black screen with mouse cursor

Try re-seating the RAM. I know how stupidly simple that sounds, but you'd be surprised! However, be sure to unplug all power!!! Even if you think the system is off, it's NOT! So unplug batteries and unplug power cords just to be sure you don't fry your RAM when you re seat it.

Even more stupid would be to forget disconnecting all USB devices (less K/B and mouse). Hopefully, I don't need to say any more there.

Then check the BIOS which I believe you said you did. But I have a problem when you say all you can do is manipulate the boot order since that's not likely the BIOS settings. Personally, I've never seen a BIOS where the date and time couldn't be adjusted. So if you can't at least set the date and time then I'd bet dollars to doughnuts that you're not really in the BIOS. Typically, you press the DEL key shortly after powering on to get into the BIOS. But that key could instead be something else like the ESC key or F1, or F2. (Sorry, I can't recall what Sony typically sets it to.) And once in the BIOS you might want to pay attention to all areas related to RAM and CPU functions. This is a whole other area of discussion but just know that even one bad setting can result in a very sluggish system.

Next you might want to check all connections and make sure you don't have a failing hard drive or something. Cause from what you said, it sounds quite likely that your HDD may be on it's last legs. (Hopefully, you have things backed up too.) Then again, you may just need to re-partition and/or re-format (which will kill everything on it). So before you do anything else, you may want to check with the HDD manufacturer and see if there isn't a diagnostic boot disk you can get (usually by downloading an .iso file and then burning it to a CD that you then boot with).

One other suggestion might be to try booting a live Ubuntu CD (which is pretty much done exactly the same way where you download an .iso file and then burn it to CD that you then boot with). And in case you didn't know, you can boot to a fully functioning (although somewhat sluggish) system when booting from a live Linux distribution such as Ubuntu. So if you can at least do that much then it's almost a guarantee that you have bad HDD or some other SATA/PATA controller issues.

I can't say if any of that would work, but those would be my first steps. Good luck...