I should have said this earlier - welcome to BC !
I still think a system restore is your easiest starting point. Click 'Start - Control panel - System' and then in the top left hand corner of the system screen click on 'System protection'. In the box that appears, click 'System restore' and just follow it from there. When the restore is finished, you may need to re-boot.
I googled this computer - that's why the make and model is useful - and it was a well received business desktop when it was released. However, this means that your computer was probably built between 2008 and 2010 and the possibility exists that it is beginning to show signs of age. Like Amythyr, I think you could have a graphics problem. If the restore doesn't fix your problem, then go to the HP web-site and download the latest graphic drivers for your computer and install them.
If you still have this smearing after that, then you are probably looking at installing a separate video card. According to the review I read there should certainly be room for a basic video card, which are not expensive, and in any case will give you better graphics performance than the on-board graphics this computer came with. You could always see if a friend would lend you one to try before you buy.