Just did I quick Google search to see if there are any known issues with this PC, and I found like 2 discussion threads about having boot-up issues: (one listed below)
http://forums.computerrepair.com/viewtopic.php?t=666
Which was what I was thinking it may be, a hardware over-heating issue.
If that is the problem, it usually happens if you leave the PC on for a long period of time, which actually decreases as you start having the problem more frequently. My issue was mainly b/c my PC was located on the carpent floor where I frequently vacuumed. And with having the PC on all the time, as I do, the fans would suck in dust and carpet particles and over time (about 2yrs really) that was too much and the CPU would began to over-heat. This caused mine to shutdown automatically, and I had to just finally pop the hood and clear the CPU, fan and heat-sink -- but it fixed it.
Now yours may not be to that point, but if over-heating is a slight problem, you have those time of start-up issues as it tries to cool before booting up.
The other reason I'm talking about the cable modem is because of two reasons... a virus (though I know you have ran the scan, but since I don't like Mcafee, I tend to discredit it
). A virus or an attacker could have your PC "under-siege" where it reboots or fails to start when the modem is attached. No likely the problem, but could still tell us something if it stops when you turn the cable modem off. The second of the two reasons for the cable modem is the way you may have it connected.
Is it connected directly to the NIC card (network card) or does it have the Ethernet to USB adapter? Reason being, i've used them both and for some odd freakin' reason, sometimes (and I do think I know why, though I can't fix it!) when its connected directly to the NIC, the modem sometimes prevents it from shuting down, but may work in reverse and prevent it from booting up. Either way, since I don't know the complete history or chain of events, this would be a test (powering off the modem that is).
Now after that is all said, YOU can just go back to the above post and do those two things
.
I listed my reasons for the others "Techie" cats that may have ideas as well.
-- Later!!