If you can get Windows98 onto the laptop then you should be jamming, however 98 is not ideal for USB devices like external floppies, besides 98se is about 240mb IIRC.
So, get an RS232 cable and a copy of Laplink (freeware). This will let you link up to your main PC, and transfer files directly.
This is old school stuff, but your dealing with an old-school computer (a pun, I made another pun!). Once you have 98se installed, just boot into DOS and run that setup file.
But, you do still need drivers, so investigate sites like Driverguide.com for as many drivers as you can get before you start, then you can laplink them as well.
Your battery, well take it out of the laptop and throw it down the street. It's probably 10 years old, there's nothing it can do for the laptop now, resign yourself to the fact that...
a) You can only use the laptop when it's plugged in.
b) If someone trips on the power lead the laptop will shut down, all the battery could do is act as a non-reliable powersaver.
c) The laptop is probably so ugly that you wouldn't want to be seen in public with it anyway.
Aegrescit medendo