Can you suggest PC specifications for working with large Excel files?

What are you using now?  You can go to 'My Computer' or 'Computer', right-click on it and choose properties and it will show you 2 important things:  what CPU/speed is in the computer and how much memory is in it.

From what I've seen with Excel 2010 with very large files, with lots going on, you can probably not worry about RAM above 6 GB.  Excel doesn't seem to use that much very often at all.  I have a 12 GB system, and no matter what I do, it seems there's always at least 6 GB available.  But RAM is relatively inexpensive so go for at least 8 GB - more won't hurt, I'm sure someone will come up for a use for it in the future.

Spend your dollars on the CPU and buy some speed.  If you are looking at Intel based systems, look at i7 CPUs up in the 3.4-3.6GHz range.  If you really want to spend some OUCH! sized dollars, look into systems using the Intel Xeon CPU - actually architectured for server use, they are more powerful than even an i7 running at the same clock speed, but you pay dearly for the luxury because systems with those in it are usually targeting the business market, not the home users.

Give strong consideration before throwing dollars and hardware at your problem.  It is NOT guaranteed to fix it.  I have a 3.6 GHz i7 CPU with 12 GB RAM on a system with several terabytes of fast hard drive storage and I sometimes run into the very same problems that you are having: Excel shows "(Not Responding)" for a long time - and sometimes (rarely, but it does happen) it just seems that the only thing to do is use the Task Manager to kill it and try again.

You typically see the "(Not Responding)" notice when the computer is really tied up recalculating the formulas in the workbook.  All of this depends more on the complexity of the formulas and how you've designed your workbook than it does on quantity; although obviously quantity still plays into it. 

Charles Williams, an Excel MVP, has done a lot of research into how Excel actually functions internally and has written a lot about how to structure a workbook for best performance.  His site also has some tools available to help you identify where bottlenecks in the processing might be found.  You should check his site out - the reading, and some of the tools, are free which is a much better price than you're going to get on a new computer:

http://www.decisionmodels.com/index.htm