The external drive should be quite safe as regards the protection of the contents with a catastrophic failure in the computer.

Is this a laptop or desktop?
I assume you do not keep the external plugged in all the time?
Are the noises beeps or other sounds from the speakers or more a mechanical or grinding type sound?

Thanks, Owbist. My computer is a desktop and I do not keep the external drive plugged in all the time- only when I want to use it. The noise, which is not constant but occasional, is a grinding noise. I get so disgusted that sometimes I hit the computer and that usually stops the noise till the next time it happens. I just can't help wondering if it's about to crash.

How old is the confuser?
Have you ever had the side off and cleaned out the dust bunnies?
Does the computer sit on the floor? It should be up 5 or 6 inches to help keep dust out that has settled on the floor.
If a hit corrects it then it might be a loose wire touching the fan blades, it could be the fan failing. Either of these are easy fixes. Maybe even a vibration causing the sound.

My computer is 8 years old. It sits on the desk beside the monitor and keyboard and was cleaned about 3 years ago. There is no one here who could help me with some of the upkeep but I realize there are things that need to be done.
I guess if I want to keep the XP a while longer I should see about some upkeep.

No no, not necessarily. We can only answer questions based on info provided and you are providing a picture of the set up.

I am not sure with your Compaq but there might be a lever type thing at the top rear. Play with this to loosen one side so it can be removed. If this lever is not there then perhaps you have 2 screws holding each side panel on. If you have a Phillips screwdriver you can remove them from one side and slide the side panel back slightly and it should come off easily then. Shut down and remove the power cable from the rear of the tower first of course. Then have a squint inside to see how much dust is on the fan and the cooling fins underneath it. Perhaps if you are not living in a dusty area it may well be clean enough. Look around for a wire or other cable that might be loose enough to vibrate against something to create the noise you hear.

I've heard grinding noises from hard drives before they die. Or, less frequently, from fans (blades hitting something as they spin, though that typically doesn't sound like a grinding sound). There are really no other moving parts inside.

Owbist, I will have a better look at the computer tomorrow in the daylight but it looks like there are screws that have to be removed. Our son will be over this weekend so he can loosen the screws for me. I'll have a look inside and let you know what I see.
Snidely, I had heard that grinding noises can be a sign of a hard drive failure. My computer makes humming and grinding noises after rebooting but usually settles down after two or three minutes-

Is the hard drive activity light illuminated when you hear the noise, or not illuminated? That could be a hint of the source.

Snidely, I rebooted to see what would happen and yes, the activity light works as it reboots. However, the noise is now ongoing- But I will try taking the side of the case off today and see what is happening.

fwiw
I have a little self powered usb drive case... stuck my old laptop hard drive in it. I use it as an external drive for a weekly or so image of my newer laptop system drive.

Mind you this is a 12 dollar external drive case -- it will corrupt the external drive if I crash windows with it connected. Next time you plug in that portable drive, windows tells you its bad.

I can fix it but it takes some effort usually.
Have to plug it in hot, shut/power down completely & a fresh start to get it back recognized and then it maybe or maybe not recognized as an additional system boot drive. Takes some effort to make it work as a portable usb drive again when you're in a hurry.

Mikie, I don't think I'm ready for that- Thanks for the idea though. I haven't had time to open the computer case yet but will get around to it soon. There have been no more noises so maybe it has settled down for the time being. Thanks to you all for your help.