Hi
I actually have a number of T1910 Toshiba laptops (unlike the guys giving general well meaning advice above).
It is a complicated matter to replace to the Toshiba CMOS backup battery in the T1910.
It requires a very careful and lengthy dis-assembly of the unit to reach the battery.
Unfortunately the service guides and machine breakdown charts that I have for this laptop are no longer available on the web, and information is very thin on the ground these days due to the advanced age of this i486SX based laptop.
May I suggest that you take a look at:
http://home.att.net/~ronkar/toshiba.html for general information about the T1910 and other machines in this series that share common parts, etc.
According to the dis-assembly chart that I have in front of me ("Toshiba parts catalog"- T1910 - CAFP-B940168-B01) the part you are after is: P000180060 RTC/SYSTEM BATTERY
It is a shrink wrapped battery with a fly-lead that plugs into the second (from the top) mezzanine board located at the back of the laptop.
Access to the board requires the removal of the keyboard and two top case bezels (top of case around keyboard and panel immediately behind it (beneath the screen)).
Dis-assembling these laptops is a pain. Nothing should be forced (or damage will result).
I too like my T1910 laptops. I haven't bothered to replace the batteries and simply acknowledge the boot time error and set the system date and time manually (if required). I typically use these laptops as serial comms terminals, etc, and for electronic project work (driving devices from the parallel and serial ports). They work with FreeDOS (with a few minor bugs) and are a lot of fun to play around with. Sadly though, due to their limited expandability, and the availability of cheap more modern laptop hardware they are generally BER (Beyond Economic Repair) when they fail, and spare parts are rare.
If you are keen and careful I would disassemble the laptop to extract the battery, then cut away the shrink wrap to determine the battery type, then build a replacement battery unit using an equivalent battery and the cannibalized fly-lead (making sure to insulate the battery identically to the original). But do so at your own risk.
BTW when performing this sort of work I recommend lots of plastic bags to hold the sets of screws, a notebook to record the activities, and a digital camera to record snapshots of the dis-assembly.
Hope that helps.
Regards
Chris