Just please make sure the old version of the logo is not in the video. Also I just realized I have an old version of fraps on my server. This is the last free version of fraps so it doesn't have a watermark but it also doesn't record audio. That works though if you want to put in your own, but just make sure you have the license and permission for the music.
http://platinumarts.net/fraps19d.exeFor editing I like using virtualdub though there are a lot of options (windows moviemaker and such). Virtualdub apparently can also record videos though I have never tried it.
http://www.virtualdub.org/Take care and also you can do more than one submission

Have a good day!
-mike