I have a tarot nano but I can't really advise much from the looks of it the battery is almost fused with the board and there's really nothing even to disassemble. If you left it sitting a long time with the battery almost discharged, I guess the battery may be dead, I'm assuming that could be part of your problem or if you left the tank on the vape and full, maybe some eliquid got down through the 510 pin, IDK. It sounds like an annoying problem to have. You could check and see if it's still under warranty and warranty it if it is, I guess. Otherwise, you could take it to a vape shop if you have one near you that is good with electronics and they might be able to diagnose it for you, emphasis might.
I like mine quite a bit for what it is, it's an internal battery setup and I have long accepted that it's not going to last forever, same as with any vape (although, I think many mods with removable batteries last longer, due to being able to replace the batteries, and not constant wear on the USB port and etc.
If you like it enough, maybe you will purchase another one and yes the tank should continue to work on other mods, and yes, Vapresso and other mod makers make a nice selection of other types of mods . If you like the tank on your kit, you could certainly keep it and just replace the mod, etc.
Anna