Okey-dokey, I am going to need some assistance here, please.
Firstly, you can see here from the related Purdue Engineering page even the 2007 year had Dell kick out two versions of their OptiPlex:
engineering.purdue.edu
We need to know what we're working with here.
My memory of the Vista access to some of the necessary information might be off, but roughly you should be able to do the Start to Control Panel to System (or System and Maintenance to System) and there you can give us the Processor, RAM, system type.
If you want to do a screen grab be very sure you block the Product ID or I will send my PC to lecture you. (You might think PC stands for Personal Computer, but from this work station we send out Privacy Cops and they are great at scooting through the Net lines and jumping out of your unit and standing on your monitor and lecturing you about privacy and that Product ID shouldn't be shown to non-confidants.)
Anyway, we need some information, as stated above. One big thing is system type, because a 32-bit system only goes up to a max address space of 4GB and part of that is determined for use by your BIOS and then your graphics card, so extra info is needed. Please.
Very likely there won't be anything that will cause your unit not to be able to be upgraded to W7, but taking anything for granted with this sort of work is not a good thing to do, so we check stuff first and then move on.