Easiest way to do Check Disk is to open Explorer, right click on the C drive icon, select Properties, then the Tools tab. Click the Check now... button. Put a check in each box and press the Start button. It will ask if you want to schedule this at the next restart, click yes/Ok and the restart the PC. This will do a check of the hard drive to see if it has any errors and mark them as bad and attempt to move the data off the bad sectors... This will take up to 2 hours.
Defreag, I think Vista is supposed to do it on its own, but a little help is OK. Once the Check Disk is done, go backj to that same Tools Tab in the C drive Properties and click the Defragment now... button. Select the C drive and click the Defragment disk button... Walk away again for an hour...
Before or after these 2, go to the HP support site and look up your system... the image you posted has the model number, you just also need the Pavilion or whatever it says on the front of the case with that model number. Once you get into the menus, select the type of Vista you have (again in that svreen shot) and then look for something labeled BIOS or Firmware... Download it and run it.. Now your system is (hardware wise) as good as it can be.
Now do the Windows Updates. Should be an icon on the Start Menu... Do everything that is there... Windows Critical, and optional. I'd leave the Bing crap and the Windows Search tool off the system... Run the Updates theough, rebooting until there are just the Bing and Search ones left... Now Vista is up to date.
If it still is messing up... Pull the Hard Drive out and donate it and get a new system...