I run AVG & SpyBot on all my machines without any difficulty...except for really old, slow machines. I just installed Win XP SP3 on a 500MHz Celeron with only 192MB of RAM, and in order for this to run acceptably I had to disable AVG's scheduled scans, and most importantly, disable TeaTimer. TeaTimer is a resident process which monitors in real time all other processes for potential registry access - this can really bog down an old machine. I had exactly the same symptoms you're having.
To disable TeaTimer, first uncheck all the TeaTimer options in the SpyBot icon on the system bar. Next, you can either run msconfig and uncheck TeaTimer on the Startup tab, or better yet, use an applet like "Startup Control Panel" from
www.mlin.net, which is far better than modifying the load sequence from msconfig. Also, don't stop TeaTimer from TaskManager - that can result in an unstable system. Just disable it in the startup sequence, then reboot. I think you can also just disable TeaTimer directly in SpyBot from Mode->Advanced mode->Tools->Resident.
Also, be aware of what you're losing: TeaTimer is a significant aspect of SpyBot...but if it makes the machine unusable it's better to disable it.
Disabling the AVG scheduled scan is, in my view, the best option anyway. Just manually start a scan when you're not going to be using the machine for a bit. You can tell when it's scanning because the AVG icon will have a white triangle in it.