So is there any where I can dispose of batteries?
I’ve got a dead laptop battery that I’d rather not just throw in the trash.
Do you think any of the vendors at BaDe Lu would take it and actually do something with it? or would they end up tossing it. 
Stores like 7-11 have special bins you can use to dispose batteries in, they’re usually located next to the photocopier or you can just ask the clerks to help you out.
Many MRT stations in Taipei also have a small container (shaped like a big D battery) to drop your dead batteries in. Not big enough for a laptop battery but handy for smaller ones.
You could try to open the battery case carefully to get access to the individual cells, those are standard size.
I really wouldn’t recommend this. You’d need to chop up the case and cut wires/desolder cells to do it and Lithium Ion batteries can explode if you short them out or puncture them. Plus the people collecting the batteries won’t be expecting LiIon batteries. And they might get shorted out inside the bin.