can't set screen resolution

That's why I would suggest another monitor to test. If it is ok on a different monitor the NEC may just be incompatible. It seems you have tried everything I could offer as I don't know precisely what is in this custom build in an HP case. If a video card is installed I would need to know what model. if it is integrated graphics (built into motherboard) I would need Motherboard Model. We could try updating the graphics drivers but again it would be best if we knew what type and model numbers we are talking about here. Any warranty on the custom build? Might be a good idea to contact that shop and see what they can offer.

Here is a link to the Intel download page for that chipset. It shows support for up to windows 7 64bit.
I would download the correct driver for your version of windows. 64 or 32 bit then
Uninstall the current graphics card via the management console and be sure to check the box that says remove driver. install the new driver before rebooting to keep windows from automatically installing their own driver.

Ok you can try reentering the chipset model where indicated. I found windows seven 64bit on that page. It might be because you used their diagnostic tool. you can try clearing cookies before proceeding to that page. If these drivers don't work I would suggest contacting the builder and taking in the monitor as well to show them what is happening. It sounds like they did a Frankenstein build and hopefully have a warranty.

Sorry for the delay. It has been a busy day already. If you are going to install a PCI card then the only thing you truly need to remove is any program associated with the current graphics adapter. your bios should automatically disable the on board graphics and send its data to the new PCI card. Once booted in VGA mode If online the OS will look for drivers via the internet. If you prefer to use specific drivers then unplug the internet connection prior to booting with the new card. Be sure to have either the dvd/cd or download ready.