Total system lockups of the sort where the mouse and keyboard are completely unresponsive come down to one of two causes: a bad driver
or broken hardware. I suspect the former in your case, given that it always seems to occur in a very specific place - when you navigate away from your homepage. Bad hardware would generally be more likely to manifest itself in a range of symptoms, including multiple different crashes and unreproducible badness. That's not always the case though; your problem may still be borked hardware.
The OS prioritises everything it does internally with a priority scale called the "interrupt request level" (IRQL). A USB keyboard and mouse may operate at IRQL=2, while your NIC and NIC driver (just as an example), may be assigned say IRQL=17. While the NIC is doing stuff, the mouse and keyboard and everything else lower in priority than the NIC will just have to wait. A common cause of lockups is when a driver goes ga-ga at high IRQL and thus effectively cuts off the mouse and keyboard, and almost everything else. That can happen because of bugs in the driver, or because of hardware-level problems with the device which it represents.
If you're currently using a USB keyboard but you've got access to one with a PS/2 connector, try using the PS/2 keyboard for a while. It will do its thing at a much higher IRQL and perhaps give you more control of the machine the next time the problem occurs. That's not a fix, just something to try for a bit of a laugh
More usefully, try booting to [safe mode + net] and testing to see whether the same issue happens there. If not, you have (almost) proof positive of a software problem.
Unless the regsvr32.exe crashes always seem to accompany every instance of a lockup, they're unlikely to be related. My gut feeling is that your lockups have nothing to do with regsvr32.