Unfortunately in situations like yours it's extremely hard to determine the faulty component(s) and maybe impossible to fix if any of the tiny SMDs (surface mounted devices) are damaged.
The battery issue does strongly suggest something like this. A little elaboration:
BIOS settings are kept in the volatile memory by means of stand-by 5V voltage from the PSU. The 3V battery is only meant as a backup during power shortage, unit displacement - anything that may interrupt the power for even the shortest amount of time.
As such, there is a relatively simple circuitry that switches between stand-by voltage and battery voltage as needed, in order to keep the volatile memory of the BIOS powered at all times. Usually it's one or two transistors, a few resistors, maybe diodes and capacitors.
Now, if that circuitry becomes defective for some reason, it can block the power from both the PSU and the battery, thus putting the BIOS chip in an emergency state. Sometimes it can deplete the battery in a very short time due to a shortcircuit.
Such defect may only be repaired by qualified personnel, if there's anybody out there that still cares for fixing motherboards and other similar devices (such as mobile phones, for example). Unless you personally have the skills and the appropriate tools, of course.
The fact that the board is flimsy as you say may have lead to PCB tracks breaking as I mentioned above. Those tracks are so thin that the slightest bend can break them and it's not only the visible ones on both sides but there are also a couple or more internal layers where tracks can break or blow due to high current (shortcircuit or heavy load).
The northbridge fan may not be a problem, at least not in the early boot stage. That one can easily be cleaned and greased (usually), just be careful with the flexible safety (dunno its actual name) on the axle, not to break or lose it - it tends to spring away.
It is kinda curious though to employ a fan but not a heatsink - it usually happens the other way around. I have a relatively new machine here donated by a friend (with a Gigabyte board, incidentally) which sports a quite large heatsink for its chipset but no fan; I've had intermittent crashes/reboots with it, inability to detect the IDE drive in BIOS and - coincidentally, maybe? - it all went back to normal after I attached a small fan to that heatsink which used to get really, really hot. Here it is: GA-M55S-S3 rev1.1.
Anyway, since that board will be spare when the new one arrives, you may play with it as you like but still be gentle, try not to consider it dead until it actually dies. Good luck!
Edited by Drugwash, Yesterday, 07:29 AM.