PP won't do it.
I read good things about CamStudio (though I've never actually used it). The issue is to record in a format that PP can use for editing. A lot of (most?) screen-capture program just don't do that. They record to something weird that PP can't use. I'm told CamStudio can record using the free Lagarith codec, which is an excellent quality, lossless codec that works fine in PP.
Screen Capture Notes/Problems
Free Open Source software http://camstudio.org/
-use with Lossless Lagarith http://forums.adobe.com/thread/875797
Some of these notes are for Premiere Elements, but may help with PPro
Fraps & Elements http://forums.adobe.com/thread/967201
-and Elements preset http://forums.adobe.com/thread/943772
-and more Elements http://forums.adobe.com/thread/871095
-and Lagarith Codec http://forums.adobe.com/thread/1287577
Techsmith codec http://forums.adobe.com/message/3692768
BB Flashback http://forums.adobe.com/thread/1074014
XSplit recorder http://forums.adobe.com/thread/1160940
Elgato http://forums.adobe.com/thread/1163126 w/picture
Bandicam read #10 http://forums.adobe.com/thread/954394
Tech smith are the producers of the Camtasia product line.
They have Snagit which is a cut down version, it is also much cheaper than Camtasia. I have it and with it you can capture full HD.
Take a look at CaptureWiz -- http://www.pixelmetrics.com/
I use it all the time -- it's very flexible, easy, and not pricey.
It will convert the screen cap to any codec I want and have installed, such as UT video and Lagarith, both of which work well with Pr Pro.