Does this happen after you come out of sleep/hibernate? My HP hates going to sleep, so when I wake it up... depending on how long it's been asleep, it runs like total shit and I have to restart it. Try disabling sleep and hibernate if you think that's what it is. Depending on the computer, it may not like it. Mine is fine if it falls asleep for a little bit, but gets worse the longer I leave it.
Running Malwarebytes and checking for spyware is also a really great suggestion. You really need spyware protection anyway. I use Spyware blaster, but it only works with Firefox/Ie. It doesn't support Chrome yet... they're working on it. It keeps my computer squeaky clean... it's passive protection that runs innoculation, isn't a background process... which I like. You still need a scanner like Malware bytes though to check every once in a while. I don't think it comes with innoculation...
You really need to take a look at Task Manager (Ctrl+Alt+Del) the next time you get slowness. It's the only way to be able to find the problem process if there is one... otherwise, we can't really help. If you see nothing using CPU massively (slowdown probably means something is running at 100%), then you might have a system problem. That could be spyware. If you see nothing, then that could also be the system process, like the bad sleep issue I get, acting like there is a massive memory leak somewhere, but no underlying software problem. It could also be a software issue... just a bad programming error with something you are run that only occasionally causes issues. I've had 100% CPU usage happen with Google Talk... a low impact program ironically.
