I use to service the Fujitsu Team POS 2000 and 3000 systems at prior job.
The motherboards in the ones that I serviced were no different than the low security of a standard desktop computer were if a password was set to bios you could simply remove the CMOS battery or move jumper to reset bios, and upon doing so if the system was healthy you were able to boot it and install fresh to it.
The hardware in these systems most of them were sold with weak processors. Store I worked at I tried to get them to spend the extra for the Pentium processor vs the cheaper Celerons, but they got the Celerons that were slightly slower in operation and touch screen menu had some lag compared to the Pentium CPU model that we demo'd side by side prior to purchase of the POS systems.
The fact that you have all these other issues after the CMOS battery shorted, I believe the system all along had the other issues and you successfully cleared the password which was the first process prior to all other bios checks at post.
Here is the manual if you need it:
https://www.fujitsu.com/downloads/SOL/fai/retailing/support/tp3kxl2/TeamPoS3000XL_XL2IM_Manual.pdfI'd remove the RAM that is in it and install a single known good fresh stick of RAM into it and see is this corrects the memory issue.
Not sure the history of this system but it might be why you have it now is because it has a main board issue with memory controller or something, but if you still have this system try the RAM trick and see if you can get it to post successfully.