---IMPORTANT NOTE: This procedure is much more complicated than replacing the battery in a modern system. Please read through the entire Instructable before starting. Also, this repair is designed to meet the original factory specification for this computer. If you just want to change the battery–and don't mind slightly changing the appearance of a rarely-seen area inside the computer–then there are much simpler options. See "Alternatives" at the end of this Instructable.
Step 1: Supplies
–Replacement battery, 1/2AA, 3.6V, axial leads. (Tadiran TL-5101/P)–Digi-Key, www.digikey.com, P/N 439-1003-ND
–Soldering iron, 20-40 watts, fine tip–Radio Shack
–Solder, 60/40 tin-lead–Radio Shack
–Desoldering bulb, wick, or pump–Radio Shack
NOTE: DON'T substitute other battery types. Most seemingly similar batteries (even with the same nominal voltage) won't work properly, may damage your computer and could even pose a fire hazard.
Step 2: Getting Started
The components are very sensitive to static electricity, so use an antistatic wrist strap or floor mat connected to a good ground.
Gather all your tools and materials.
Step 3: Disassembly
Now we need to remove the motherboard. (Phew. Remember what I said about complexity?) The battery is, as you can see, located beneath the power supply, but we need to access the underside of the board to remove it. Turn the machine over and detach the front panel by carefully pushing back the three large plastic tabs, marked with yellow arrows in the picture. Turn it right side up again, and unfasten the board by applying SLIGHT upward pressure and carefully pushing back the seven small plastic tabs shown with red arrows, starting at the front. The board simply swings up towards the back and slides out.
Step 4: Replace Battery
Bend the leads of the new battery to match the spacing of the holes. Make sure the holes are clean, then insert the leads of the new battery. Make absolutely sure the polarity is correct BEFORE touching the leads to the holes, and do not allow them to brush against anything else while doing this. Remember that the battery is supplying voltage even during the installation process and an improper connection could burn out components on the motherboard.
Solder the new battery into place, again being careful not to overheat the board. Make certain you do not create any solder bridges, either. Trim the leads close to the solder, making sure the tool does not cause a short circuit to any other connection.
Step 5: Reassembly
Snap the motherboard into the case by first aligning the connectors on the back edge with their respective holes, then hinging the board down and carefully snapping it into place. Avoid bending the board or using excessive force, and check to make sure all of the tabs are engaged. Then snap the front panel into place, making sure the speaker wires are properly routed under it. Snap the power supply into place, and reconnect the internal wires (power, speaker, and fan). Reinsert your cards in their respective slots. (You did number them, right?) Snap the cover back on.
You're almost done!
Step 6: Setup and Test
Step 7: Alternatives
1. Instead of desoldering the original battery, simply cut the leads close to the battery, and twist the new leads onto them. It's best to solder the connections but not actually required as long as they are twisted securely. Just be careful not to put too much stress on the connection between lead stub and board. The advantage of this method is that the board need not be removed from the case–you need only take out the power supply, in order to access the battery. As a cautionary note, make sure the battery sits flat on the board and that the twisted connections do not protrude above the top of the battery. Otherwise they might short out against the metal case of the power supply.
2. Use either of the above procedures to install a 1/2AA battery holder, and buy the version of the cell without leads. This makes it easier to replace the battery in the future.
Other hacks, such as using a different battery or adding some other type of standby power supply and dispensing with the battery altogether are beyond the scope of this Instructable and are not recommended unless you are very familiar with this computer, your intended power source and electronics in general, but in that case you wouldn't need the Instructable in the first place, now would you?
Also, make no attempt to connect a new battery (or other power supply) without first removing the dead battery. Doing so will cause reverse charging and is hazardous.
Technically there is one more option, and that is to just live with it and not do anything. But as a perfectionist myself I wouldn't consider that much of an option :)
Hope you liked what you saw and feel free to comment!