Help is usually a Google Search away. =D\

Lsass.exe is part of Windows... It could be infected, but I'd leave it alone for now and try one of the removal instructions listed on the Google search above.

Sounds like it could be a dying hard drive. Especially if suddenly it was empty. Usually the rule of thumb with BSOD's is if you reinstalled Windows and they're still happening it's unlikely it's a software problem (possibly could be software/drivers you install again after reinstalling Windows). I'd another HDD (no harm in more space!) or disable all programs that start up when your pc does. Start -> Run -> Msconfig -> Selective Startup -> uncheck load start up items. Then update all your drivers to the latest. Run it for a bit like that and see if it's still blue screening. If so it's even more likely it's a hardware problem.

You kinda have to test it on another PC especially if all 4 ports on the modem yield the same result. If it works fine on another PC it's your network card on your PC, which is not Verizon's problem. If it does the same thing on another PC, then call them back, tell them what you've done, and if the modem is still under warranty/rented they should replace it.

As for the PC speaker issue. I'd suggest looking in the bags that came in the case. Sometimes they don't include a cord for attaching to the motherboard's pc speaker header. Instead they'll put the speaker in one of the bags the screws came in. Then you just plug it into the header and it just hangs there, almost like a tumor.