The System.Diagnostics assembly is part of the Silverlight CLR framework, but it only includes classes related to debugging, the Process class is not available. Is there any
There is no short answers, but there is a complex one...
If you are runnign SL4 Out-Of-Browser, and you indicated that you are ok running elivated (which really mean SL doesnt run in IE-Protected mode, but rather as standard app...) there is a way for you by using WMI to basically do ANY THING you want to. This blog post will help you - http://justinangel.net/CuttingEdgeSilverlight4ComFeatures . Just keep in mind, this is high end fancy coding, so watch yourself ;)
There are two great sample chapters on Windows Phone and Silverlight for Windows Phone on the LearningWindosPhone.com site. There is great Windows Phone Trainng material , and dont forget the Windows Phone Develoeprs Blog