sorry didnt read the end of the other post. it could be that your battery isn't holding any charge, if your using certain battery cells in the battery (very common cells) that a drop such as the one you encountered could reverse the memory effect that the cells in the battery use to hold a charge.
So the drop of the labtop could of effected the way the battery operates, if it uses Nickel Codium cells (NiCd cells). This would explain why your battery can function for a certain amount of time, but then gives out.
What could be happening is that the batterys memory effect is not completly ruined, so it has a small amount of mah it can store. So your 1000 mah battery to 3000 mah battery (depends on which battery you have) it could only be storing 5 or 6 mah. So it has enough power to boot up windows, or boot up to a certain point, but when the parts start requiring more power, thus your computer battery gives out, and restarts. Then it realizes that it has enough power to boot up again, so it does, then once the parts start requring more power again after login it gives out and the comp restarts.
Something similar HAS happened to me in a Nickle Codium (NicD) cell battery before, although it does take a hard hit to happen, worth a shot to try another battery.
If your battery uses NiMh cells (i forget what that one stands for), it could simply be damaged battery cells, since NiMh cells don't use the memory effect.