After reading through the specs of this computer; the first thing I noticed is that uses integrated graphics (http://www.mepis.org/docs/en/index.php/Integrated_versus_Dedicated_Graphics)
This results in poor performance as your graphics are sharing memory with your CPU, as well as with the rest of your system.
You might also want to check out: Start-All Programs-HP Hardware Diagnostic Tools; and/ or HP Total Care Advisor, see if these applications help you.
FOREWORD: Before you ask, yes, I have Googled this query and came up with a couple hundred completely different answers. The countless I have tried or attempted to try didn't work or weren't applicable.
PROBLEM: Error message on upper window frame "NOT RESPONDING". At first, this seemed to occur only when using Firefox and only if I was at a graphic intense site with a lot of Flash for example. Turns out, not so. Any app that takes a slightly higher than normal amount of CPU power will temporarily freeze up, give the not responding message, then after a little wait time, continue. Prime example, I use File Shredder to do my deleting (the free app) of anything from a simple Notepad file to a 7.5GB video file and higher. My preference is the DOD method (3 wipes). On occasion, it will be in the middle of a large file shred and freeze completely. I'll then have to open Process Explorer to kill the task manually. Same solution for Firefox by the way.
I'm thinking hardware, but all diagnosis seems to come back just fine.
PC: HP Pavillion Model: a6658f
Intel Core 2 Duo (Quad core)Q6600 @2.40GHz
6 GB RAM
64 bit system
Windows Experience Index rating is 3.3 Any significance?
If you are familiar with this problem, PLEASE advise as this is truly ruining the whole computer experience!