Are these your own files that you uploaded to YouTube? YouTube typically converts the upload to flash format. And, if you download your own uploaded content, it typically comes as an .mp4 file. Other than that, I believe the YouTube Licensing Agreement needs to be looked at for using its videos.
So, first question...what are the properties of your source media and what project preset in the new project dialog are you setting for this project? If you really do have a file with an .avi file extension, what kind of .avi have you? AVI is just a wrapper format for the video and audio compression.
Is your video card driver up to date according to the web site of the manufacturer of the video card? Do you have the latest version of QuickTime installed on your computer with Premiere Elements 7 Are you running Premiere Elements 7 as Run As Administrator or from a User Account with Administrative Privileges?
When you are working with your source media on the Timeline, are you looking at the rendered or unrendered Timeline content playback in the Edit Mode monitor? Any red lines over the Timeline content while you are playing back that content in the monitor?
What do your computer resources look like and what is the size of this project....when you get to Share/Disc/DVD disc, what does the burn dialog say for Space Required and Bitrate?
Let us start here and then we can progress according to your details.
>AVI files I pulled from Youtube
Codec & Format information, with 2 links inside to read
-read both links in reply #1 http://forums.adobe.com/thread/1270588
Report back with the codec details of your file, use the programs below... A screen shot works well to SHOW people what you are doing