The only error that could have occurred with my reinstall were from the fact that I didn't remove registry keys (that may not have been removed by the uninstaller, which apparently included my registration information, since I didn't have to reset it after I started up the fresh 6.35. I did have to reset all of my other settings though.)
I haven't tried using it without SSL or without installing SSL. Unfortunately, I'm too paranoid to use mIRC without SSL. I installed SSL by running the openssl-0.9.8k-setup.exe package as linked here:
http://www.mirc.com/ssl.html. And setting it to install in the /program files/mirc folder. No other changes were made during the install process and it's the same install process I used when I first installed it with 6.3.
I'd also like to reiterate that the indefinite hangs are occurring while I am idle, not during start-up, connect, quit, close or activity (including having the window active).
Also, thank you for your response.