Hmmm this could be any number of problems.
You're computer is old, So even with anti-virus running you have probably picked up a good deal of crap over the years.
Have a look at your task manager.
Shut down all programs,
Check your system tray and shut down anything that is running in the background too.
Now when you press ctrl-alt-del, to bring up your task manager, have a look at how much RAM and CPU usage your PC is ussing while "idle"
If it seems like a high number then chances are you have some not so nice programs running on your PC.
Hardware wise, one of 3 things may have happened and are worth checking / fixing.
1st - your BIOS is probably very out of date.
Find out which MOBO you have - and get the latest BIOS update.
You may find this fixes problems such as the intermitent DVD drive.
(If you are not confident updating your bios - look on the internet how to do it, it's fairly simple, As you don't have a Gigabyte MOBO there is a small chance you can brick you're board, but only if something goes horribly wrong, so don't do it in a lightning storm
When a computer suddenly shuts down out of the blue, one of the causes can be that it is overheating, And the fact that it did not turn on for 5 minutes suggests this may be the case.
I think perhaps when you dropped your CPU the HeatSink may have moved a bit, causing a gap between the heatsink and chip.
To test this switch on your PC and boot into the BIOS (hold del or some shit as it boots)
In the BIOS navigate to the bit where you can see the temps.
running in BIOS your CPU temp should be little above room temperature.
Though even if you had no heatsink at all the chip does not really generate that much heat when in BIOS (as it's doing naff all)
on the same page (probably) you will find a setting that enables you to set a buzzer alarm for temperature.
Set this, and set it at about 70C
Your chip can happily run at this temp but it shouldn't be doing so unless you are really pushing it.
Boot into windows, and wait.
Does the alarm go off?
now start doing a few things,
Does the alarm go off?
What speed is the fan spinning at?
Is it going mental right from the off?
This would indicate that your heatsink is not doing it's job properly.
Finally it could be a loose connection, (though i doubt it) - is everything plugged in tight, check
I would recoomend you take the follwing action on your PC.
1. get acces to an external HDD - back everything you want to keep onto this HDD -
2. Download all the latest drivers and BIOS drivers etc. and put them on a USB stick.
UPDATE YOUR BIOS NOW
3. Go to a computer shop and buy some thermal paste (while you are there spend a few quid on RAM, it's dirt cheap, and you can never have enough)
4. Remove your heatsink, scrape off the old paste (you can use a few drops of nail polish remover and cotton buds to get the final bits)
don't worry too much about residue, the main thing is that both surfaces are flat.
Apply the new thermal paste and re-attach your Heatsink
5. Instal you're new RAM :-)
6. Insert Windows disk - Restart computer - Re-instal Windows.
(make sure you FORMAT all HDD's to wipe them completely, make it a clean instal)
7. when windows boots, do a full windows update.
8. Install the new drivers
9 PAY MONEY FOR A GOOD ANTI-VIRUS LIKE KASPERSKY (or at least get a trial - on no account touch Norton)
10. Deep scan your external HDD - if it comes back clean, move files to your HDD
If you do this you're computer will be running better than it did when you got it new.