Without any real info, here are some random things that come to mind.
If the problem exists even while not online, such as opening a document or typing, then it probably isn't anything to do with your network. If they use a network drive, then that totally changes everything, but I find that doubtful in this situation.
Update all your software, including Java.
That computer should have no issues running the stuff you described with its current hardware. If it was bad out of the box, maybe there is a bad stick of RAM or a faulty drive. Try running the hardware diagnostic that comes on HP computers, I think it might be F11(?) on boot. You might even be able to run it from within Windows, I can't remember.
Could be a virus. Try running a full scan of
Malware Bytes and run
Hitman Pro 3.5 . The 2 programs you listed are not high on my list of effective anti-virus/malware programs, although for every 10 people you will probably get 10 opinions on that one.
You could run
CCleaner but just to clean up temp files. The registry cleaner is probably a waste of time, but if you want to run it make sure you backup first.
Check drivers? Bad drivers, especially video card drivers can make things run choppy, even a simple webpage.
Did you do a clean install of Windows 7 or upgrade from Vista? The Upgrade path from Vista is pretty good, but I know 64 bit Vista was not the most trouble free OS and some of those troubles may have migrated.
If none of that helps you could check error logs to see if there is stuff that is going wrong constantly. Doubtful for there not to be any signs of it. How much bloatware is installed, maybe remove some?