I will try and be as gentle as I can.
First what version of Pro-E are these files coming from because there might be an incompatibility
issue. Second since you are using 2007 I think that might be compatible with wildfire 2 or 3.
Next, what might ultimately work for you is if you can get the actual Pro-E files from this customer
you can call them up directly into Solidworks. I think 2007 was the first version that did this susccessfully.
Aha - this may be the issue - they did send us the ProE prt files but no matter which options I choose, the status bar just sits on "processing" and never actually opens. I see in the SW help notes that SW2007 is compatible for import from ProE 17 through 2001, and Wildfire 1 and 2.
If I ask the customer to "save as" one of these older formats, will they be able to do that for me using a newer version of ProE?
I am pretty sure that (if I remember correctly going back to my Pro-E days)
you can save back to previous versions. I would call them and see if they can do that.
How long did you wait for it to process? If everything else seems to check out, it may be that you may just need to give it a little (or a lot) more time to sort through things. You don't say how complex the files are, but sometimes importing/converting takes a long time. Hardware is faster than it used to be (5 min to open, save, or rebuild vs. an hour for one model I can think of), but the software just keeps getting "bigger" to match. Depending on the complexity of the part and the speed of my computer, I might give it at least 20 minutes to process before I concluded nothing was happening. Also, just because Task Manager says it's not responding dosn't mean SW is not still working. Try letting one go overnight (or at least while you're at lunch) and see if it's still processing in the morning, or if there is an interesting error message.