You can run both PRE7 and PRE8 on the same machine. Use PRE7 to complete your project. In general always finish a PRE project with the software version originally used to create it - you will save yourself a lot of grief that way.
If necessary you can then export your completed project as DV-AVI or HDV and import it into a PRE8 project.
Insanity is hereditary, you get it from your children
I agree with Neale. Opening in older version project in a newer version of the program nearly always leads to buggy behavior.
I'm also concerned about your computer specs. Unlike previous versions of the program, version 8 is a bit a resource hog and will not run well on a computer with less than a dual core processor. If you're editing HDV or AVCHD, you'll likely need a quad core processor or better to edit with it.
When I tried to continue working on an older project done in PrE 7 and then tried to bring it into PrE 8 I get a error window saying, "This file is not supported or the required codec is not installed."
This is odd, as CODEC's are installed in the system. If one has PrE 7 & PrE 8 on the same computer, then the exact same CODEC's are available to each.
In the PrE 7 Project, what are the details of Assets - the ones that now will not work correctly in PrE 8?
Of course, you DO want to make sure you're bringing in the video or audio and NOT the project (.prel) files into Premiere Elements 8.
Although, as I said above, even opening an older version project with version 8 can cause lots of buggy behavior.