APC Back-ups BE500U/BE350G
Received a broken backup power supply. Although a new one costs about $50, I thought I’d give this a try at repair.
First thing is to open it up, revealing the inner board and transformer (after removing the old battery)
My unit still turned on but made a constant toned beep. The online user manual indicated a fault in the battery, but maybe it was the lack of?
I decided to look for burns or blown fuses, since those are usually the first to break. 
Behold the problem! The two 30A fuses in parallel both blew. 
To confirm, I bypassed the fuses and connected a substitute battery pack( picture shows 16V but 12V worked better) and tested the unit. 
Issue fixed! The unit can output 100V AC again. I just have to buy proper fuses and a replacement battery. NOTE DO NOT OPERATE THE UNIT WITH JUST THE LI ION BATTERIES. The unit is rated at 300W output. This means the unit may pull 25A per cell. That’s too much for the cell and can cause a battery explosion. Either connect multiple cells in parallel or buy a lead acid replacement battery. Using Li-ion in this case is entirely bad as is. The unit charges lead acid and not Li-ion at 13.4V. This causes overcharge for 3S cells; 4.6V per cell. Unfortunately when I try to operate the unit with a bms, the ups starts beeping when the bms disconnects charging. I’ll revisit this project in the future to find a way to integrate Li-ion as the power source. December 30, 2017 Got back to making the battery pack. I mentioned above to buy replacement lead acid batteries or build a large li-ion version. Me, having a box full of lithium cells, decided to get to work on one! 
The configuration is pretty typical: 3S and to fit in the compartment of the unit (BE350G in this case) 6P. Unfortunately for me, I don’t have a spot welder around (I’ll build one in a future project) so I had to do the crude sand and solder method. 
When doing this method, you have to be careful not to heat up the cell. 
Finallyy everything’s together!… The results very sketchy but nonetheless with the protective circuit in, the battery was put into the unit. Results work and it powers lamps without any hiccups!
Check out [part 2] of the project where I check the performance (and eventually make it better).