I currently am waiting on my new PC components to arrive, and have an unopened OEM version of Windows 7. I plan on using that to install onto my new PC, which I'm building, which is as far as I can understand, legal. If I were to install that, and put in the product code to activate it, would I be able to install it on the computer I'm using now and still activate it? (I'm aware this is against the OEM agreement.)
If I understanding your question correctly your asking if you can install and activate your OEM version of windows 7 on your current computer. The answer is Yes you can. But then you would not be able to install and activate the same OEM license on your new computer unless the motherboard was the same.
To my knowledge the OEM license of windows 7 is tied to your Motherboard once activated. People have reported that by calling Microsoft and explaining that their motherboard has died and needed to be replaced were able to get their OEM copy re-activated on the same model motherboard.
This is from Microsoft's website...
"Q. Can a PC with an OEM Windows operating system have its motherboard upgraded and keep the same license? What if it was replaced because it was defective?
A. Generally, an end user can upgrade or replace all of the hardware components on a computer—except the motherboard—and still retain the license for the original Microsoft OEM operating system software. If the motherboard is upgraded or replaced for reasons other than a defect, then a new computer has been created. Microsoft OEM operating system software cannot be transferred to the new computer, and the license of new operating system software is required. If the motherboard is replaced because it is defective, you do not need to acquire a new operating system license for the PC as long as the replacement motherboard is the same make/model or the same manufacturer's replacement/equivalent, as defined by the manufacturer's warranty."