Which operating system are you using?
Premiere Elements 2 was designed to run on Windows XP. It may not run well on Vista, let alone Win 7.
You may be able to find version 7 or even 4 available on Amazon.com or used on eBay. (Make sure you buy a licensed copy, of course.) Version 8 is much more stable in its patched 8.01 version -- but it does have its share of resource problems, so you may want to avoid it when upgrading.
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Along with Steve's comments, there is a likelihood that the new computer has many more programs and Processes, that load at start up, especially if this is a pre-built computer, like a Dell, an HP or a Gateway. Most of those have tons of bloatware, that is not useful when doing video editing. This ARTICLE might give you tips on tracking that down and cleaning things up.
Thanks for the help, i borrowed a friends copy of Elements 4 and it runs great. Just waiting for my own copy to arrive now.
Good news and good luck when your copy arrives.