We would love to know what that error message was if it appears again.

Try this
click Start
click Control panel
click Administrative tools
click Event viewer.

Now on the left side of the new window click System.
Look down the right side for red error messages and if you double click on any another window appears with cryptic writings but there is also a link there back to MS. This will often shed some light on the issue causing you grief.

Don't stop at the first error message, scroll down a ways looking for others as they may represent a different problem.

You might also consider scanning for malware just in case that has had an effect. Do you use Superantispyware or Malwarebytes or anything similar?

Sounds like a hard drive issue since it is intermittent like that, consider saving any important data now, run a hard drive test, Google HD Tune, If we had the error it would be most helpful now it becomes more of a guessing type thing.

Save the important data first if any, before running tests in case it fails completely....

you can run a belarc and see what it says about your hard drive health, I would also check the event viewer as mentioned and do malwarebytes scans just to make sure it is not malware related.
At this point it is going to be hard to know if it was a related incident or not. The main thing now is to determine just what in the pc is causing the error.
Belarc
Malwarebytes' Anti-Malware

also check to make sure all plugs are plugged in securely and that it is not a loose plug somewhere not properly connecting at times. I would also open the pc and check for dust bunnies, they can cause all sorts of havoc in the pc if it starts getting dirty it can over heat. check for secure connections inside as well.
Cleaning the computer and its components

Thanks for the ideas everyone. As for backing up my data, what is a good, inexpensive external hard drive I can look into? I don't think I have a whole lot, maybe 5 GB. How much data can each DVD/CD hold?

DVDs about 4.7GBs
CDs-about 700MBs (way less)

Thanks again for the things to try. I'll look into it over the weekend.

I've come across something called registry cleaners. Might this be something beneficial? Or may it cause problems?

Regarding backups, which files do I back up...everything on the C: drive?

Have a great weekend!
Ryan

I would choose not to use a registry cleaner that is the advice given on most reputable computer help forums, this one an many others.......

Hard to say what you should back up because we do not know what you have. All personal data, email addresses and perhaps favourites/bookmarks of course.

As importantly is the drivers for all the motherboard stuff like sound, LAN IDE or SATA drivers. However if you have the CD that came with the motherboard they will all be there. If this is a factory built machine you should have either a recovery partition on the hard drive or CDs. If a factory built life can be easy, just start the recovery process and the computer gets returned to the state it was when it left the factory.

You will need drivers for any add on boards like a video or sound card if these are not built into the motherboard.

What make and model is this?

As Zep says, don't mess with your registry. Nothing will be improved but much could go wrong compounding your problems.

The make and model are: Lenovo 3000 J115 7387.

if you have that little to back up consider using a simple flash thumb drive they are very inexpensive and can hold a lot, I have been buying Kingston 4Gig flash drives at Big Lots for $10 just to give you an idea of the price.
I got bigger ones to do a back up of all my individual computers as just one more backup method.
another method is to use an online backup locker like Adrive they give you quite a bit of free storage space. I use their basic free plan.

Here is a link that might be useful: adrive

OK, here is that error message (it hadn't come up in a couple weeks): Invalid Kernel Handle.

When it occurs, you can't use the power button to turn off the computer; you have to unplug it. Any ideas on what it could mean?

Ryan

That's a blue screen error correct, it should look like this on the screen or something similar:

invalid kernel handle
STOP: 0x00000093 (0x00000088, 0x00000000, 0x00000000, 0x00000000)

Posting the stop error (STOP: 0x00000093)as seen above would be helpful next time it appears, these type of errors can be difficult to tract down.

You really need to run the Microsoft debugger program to gain more information about the error.

When you get a stop error (Blue Screen of Death), your system writes a small file called a minidump. This is a small write up on how to debug memory dumps. This becomes extremely useful when you are trying to figure out what caused a particular stop error, and no filename was mentioned and/or it is undocumented.

see link

Here is a link that might be useful: majorgeeks

See link possible consideration for error...

Here is a link that might be useful: support.microsoft.com