You don't give much explanation as to the problem or post any wierd error messages you found in your logs, so not much anyone is going to be able to do I don't think.
If the server seems to be hanging, its hanging on something, and (with any luck) should generate a logfile with errors or at least some info of whats going wrong.
Also, if you haven't yet, check the upgrade checklist tomake sure you're in good shape there. http://forums.cpanel.net/showthread.php?t=66166
If you can't dig up support on the forums or solve this yourself, I did read a comment by someone on cPanel staff stating that they have relaxed support tickets to most everyone right now with the new release of cPanel11, for a limited time I'm sure. Ask them, 'billing AT cpanel.net' would work I think.
...I'm going to have to say its the server or the cpanel software. both are
hanging up on me quite a bit.
This tells us nothing really. But you might like to install this, http://www.logview.org/content/view/5/26/
for easy access to your logfiles that just might.
That said, if you think it may be your router (or home firewall), that's an easy one to test. Remove/disable from the connection for a few minutes and see if you still hang when doing something on your server. It's called troubleshooting.