First guess it that your six year old copy of Premier Elements 10 needed Apple's Quicktime for the codecs. Did you install it on your new PC? Note that there are reports that Apple no longer supports Quicktime for Windows and it may have some holes in it for hackers. There are ways to install it safely, but the better choice may be to buck up and buy a new version of Premier Elements!
No have not installed but I think your second suggestion is better. Buckling up
FWIW, some versions of Premiere Elements (including version 10) did have a bit of a video lag problem, as you're seeing.
This problem was addressed in version 14 and has been virtually eliminated.
Meantime, make sure you've got the latest drivers from nVidia for your graphics card. (Don't accept the Windows driver.) And, as Bill says, make sure you have Quicktime 7's components installed, even if you opt to disable the Quicktime Player itself for security reasons.