I don't know much about BIOS, so don't hold me to this, but I have heard that a failed BIOS flashing can permanently damage a motherboard. I believe this is why it is recommended that you only flash/update your BIOS only when you're having problems with it.
If all of this started happening after the failed BIOS update, I'd venture to say that this is your problem. And, if what I've heard is correct, it may be a permanent problem with the motherboard that can not be fixed. But, once again, my knowledge of the motherboard, its components, BIOS, etc. is very limited. I'd check with the techs here and/or do a Google search to find out what you can about failed BIOS updates.
In the meantime, let me see if I can help you rule out some other possibilities:
You reinstalled each piece of hardware, but did you try removing all unnecessary pieces of hardware? Modem, sound card, network card, etc. If any of these pieces of hardware have gone bad, they may be causing the lockups. I'd suggest booting up your PC with no drives (except the hard drive of course) and no unnecessary cards (if your motherboard doesn't have an onboard video chip, you'll have to use a video card, but I'd suggest using the onboard if there is one). If it still locks up, then you know it's either the HD, motherboard, CPU, memory, or power supply (or video card, if you have it connected for the test run).
You switched around the memory sticks that are currently in your PC, but did you swap them with known working ones from a different PC? I seriously doubt all of your memory sticks went bad at once, so if it still locks up with any one in there, then it's probably not your memory...however, it's not a bad idea to borrow memory from a friend's computer that works just to be sure that it's not your memory.
As far as the capacitors...they are normally blue, or black, or purple, or even brown...but, whatever color they are, the top is metallic looking. The tops have usually three, sometimes four creases in them. These creases allow the metal tops to flex a little when a capacitor is going bad and starts to expand. This relieves a little pressure and keeps it from completely exploding, though they do pop sometimes. Basically, you're looking to see if the tops of the capacitors are bulged up. The sides very rarely bulge out, just the tops. If you see a brown buildup on the top or bottom of the capacitor, that is a sure sign that it is bad. The brown buildup is not corrosion or rust; it's part of the electrolytic fluid that is inside the capacitor. If the capacitor is only bulged out but isn't leaking, the capacitor may or may not be bad; but, if you're having strange problems out of your PC and the capacitors are bulged, I'd dare say that they are indeed bad. Generally, most people have reported the capacitors around the CPU as being the culprits that normally go bad and cause problems. However, I would check all of the capacitors just to be sure.
Again, I believe that the failed BIOS update may be your problem. However, since your computer only locks up after being completely booted, it may not be. Test out your system with only the necessary hardware, then at least you'll have it narrowed down. Then check the capacitors. If it's not either of those, you can run your PC with the case off and a fan directly on it to be extra sure it's not overheating. And if THAT doesn't work...well, it might be the power supply. That could be checked by either borrowing someone else's power supply or using a volt meter to make sure the different leads from the power supply aren't causing voltage spikes.