This is only one of two things.
1. Hardware failure (unlikely) The clock stopping could indicate hardware failure but typically hardware failure causes the computer to just suddenly and without warning reboot.
2. You have some garbage programs in your Startup list (very likely).
click "start / run / (type in) msconfig / Startup" to see the list.
A full explaination with screeshots is here - START-UP APPLICATIONS and a full list of programs is in the list or if you are good in Excel there is the list in Excel format
Don't try to user the other programs listed in the article at first, just stick with msconfig. IF cleaning up the startup list in msconfig does not fix the issue THEN go to the other programs discussed.
After you've had it turned on for a while (at least 10 or 20 minutes), turn it off, take off the side of the case, ** touch the metal chasis of the case to drain off excess static electricity ** and then move your hand around, touching places, looking for hot spots, almost too hot to keep your hand on. Look for excessive dust accumulation. Turn it back on and boot it, with the case side still off. Look for fans not spinning.
If your system is still running with reasonable cooling, with no failing fans, and no great globs of dust, then test the memory.
Go to memtest86.com and either purchase a bootable CD or download and burn a free one, as you prefer. Run that test for at least 5 or 10 hours. If it shows no errors, then I'll be surprised, and your hardware is likely in better shape than I'd have guessed. This doesn't check all the hardware, but it does get to the CPU and the memory, which covers the portion most likely to just freeze up hard.
If it finds memory errors, then it will depend on the pattern of errors what you do next.
If memtest86 passes with no errors, and if there weren't any serious cooling problems, then I'd replace the power supply with a quality, name brand power supply, such as named on http://www.rootminus1.com/howard/psuselection.html. The power rating, such as for example "600 Watts" of a power supply, and the vendor or store selling it to you, mean basically nothing. Choose one of the power supply brands on that list and accept no others. Power supplies weaken in their old age. Failing supplies masquerade as all manner of problems. The equipment to properly test a power supply costs tens or hundreds of thousands of dollars. The only option if you don't have access to that kind of lab equipment, and you have any doubt about your power supply, is to just replace it with one of these trusted brands. Read further on the above link to understand how to calculate how much power you need.
One other avenue to pursue - search on Google for the make and model of your motherboard, with words like "freeze" added to the search. For example, I had a system doing this sort of thing to me once, and after spending time over months trying to fix it, and after replacing several key components, at considerable money, I stumbled on a post that found one minor feature of the BIOS was not stable. Once I disabled that feature in the BIOS, that system became instantly as solid as a rock.