Will an Intel Core Duo E8500 3.16 ghz be able to convert from Windows 7 32-bit to 64-bit?

Download CPU-Z and look on the CPU tab.

If Code Name=Yonah, then you do not have 64bit support.

If memory serves, you should have a Code Name "Wolfdale" which supports 64bit.
 
Core 2 Duo is 64-bit whereas Core Duo (note the missing 2) is only 32-bit. Now, that said, your specs indicate a Core 2 Duo E8500 which is 64-bit and will do just fine. However, as you only have 4GB RAM you'll get no additional benefit by switching to 64-bit. Now, as there is no direct upgrade path from 32 to 64-bit (clean install only) you will need to back up your data for later restore.
 
Based on my own experience I can say that upgrading shouldn't be any problem. I am currently running Windows Home Premium 64bit with the same processor as you: the Intel Core 2 Duo E8500. So, you should be fine!
 


Thanks for answering. I have seen things about this clean install everywhere but I don't understand it or how to do it (I'm new to this)
 
A clean install is very simple.
Just plop your windows disc (or USB boot device) into the PC, Restart the PC and run from the disc/boot device.
A clean install will remove everything from your hard drive so if you have anything on there you want to keep, You will need to back them up on another storage device.
 


How do I run from the boot device? And do you mean I just get a windows 7 64-bit install disc?