Heat would explain those symptoms. The temperature inside the case gets to be too high when you're using it heavily, and/or because 2-4PM tends to be among the warmest points of the day, causing the system to shut down to prevent causing any damage to the hardware, but leaves the fan running to suck some of the hot air out.
Just to test this theory, take the cover off of the unit and run it like that for an evening, see if the situation improves. If it does, you will need to figure out how to improve air flow in your computer. Otherwise, your problem is likely something else.
Also, one spyware scanner simply isn't enough. Even if you tack on Norton's craptastic one, it's still not enough. If you're going to use high risk programs (IE, Outlook, Outlook Express, MSN Instant Messenger/Windows Live Messenger, Windows Media Player, etc) then you need to have multiple spyware scanners. No single program will catch everything, so be sure to add to that AdAware, Spybot, AVG Anti-Spyware, and even Windows Defender if you like.
I have a Dell Dimension 3000 with Windows XP2 Norton anti-Virus software and Spyware Doctor. All scans are clear of viruses and spyware. 5 days ago my computer tower started to shut down while leaving the monitor and fan still on. The only way I could restart was to unplug the power cord from the tower and replug it in then press the start button and it would come on. Everything would be normal but 10-20 mins later it would happen again. this started around the same time everyday 2pm-4pm while I was working playing music etc., full usage. Once I was done for the day in the early evening it would run without problem all night to the next day when it was on but idle.I wondered if it is overheating the power supply because it happens when I am using it more in the daytime. I am confused as to why the fan and monitor would remain on when the tower shuts down. Any insight would be appreciated I am a newbie of sorts. Thanks