I've noticed that when my PC is running that AM radio reception on my stereo in another room is destroyed - can a PC generate AM interference
Tons of it.
Have you tried tuning around? Is the interference present over the whole band, or just on one frequency?
Has it been this way for a while, or is this something new?
Added any new hardware, or even changed anything? on your pc, lately?
Changed the antenna feedline or antenna location, or the location of the receiver lately?
through the house wiring?
Possibly.
or is it somehow broadcasting?
Possibly.
I have the sides off the PC tower at the moment if that makes a difference
If your pc was radiating, I'd expect this to make the interference worse.
and my stereo is hooked up to an old fashioned rotator type antenna.
Easy thing to try: Coil up the power cord that feeds your pc. Use a rubber band and/or scotch tape to hold it in shape. See if that makes a difference.
Other thing to try: Ferrite beads. If it were me, I'd go to some geeky radio hardware type friends and ask. For you, - you might want to try googling for them. Somebody, somewhere should sell them. If they are cheap enough, it would be a good experiment.
Both of these ideas are attempting to stop RF from getting out on the power cord of the pc.
You could try them on the power cord of the AM reciever too.
By the way, are you using either a surge protector or a UPS for the computer? If not, borrow one of each and try them. Especially the UPS.
If you suspect that the pc box itself is radiating ( do you have a portable hand held battery powered AM reciever that you can hold near the case?)
be sure the case is properly grounded when the computer is plugged in to the wall.
Could be a lot of ways to lose ground. The third prong on the power cord plug is ground. Maybe the wall socket has lost ground? Maybe somehow inside the power supply it has come loose? ( Caution: if you are not technically savvy on the workings of power supplies, it is best if you do not open the unit. There are harmful voltages in there. )
Pull the plug from out from the wall before doing any looking around!
Are you using an extension cord? Try a different length. In effect - meaning try a different length of power cord. You could have accidentally achieved some kind of resonant length.
These are just a few things that come to mind.
Keep us posted.