Recall was only for 2008 Gen 1.. first 6 months of production and is now well and truly expired.. Apple no longer extend warranty on any TC.
The fault depends on the model.. look at the rubber foot. Is it A1355, that would correspond to 2010?? Earlier ones are more likely power supply.. Gen 2 is A1302. For Gen 3 it can be a number of issues.. could be a dead power supply.. but also dead boards are common.
See info here.
Unfortunately Apple do not repair.. if you have applecare on a computer it will be replaced. Otherwise find an electronics technician.. if any still exist. So much stuff is made is not repairable we all went out of business.
If the disk inside is removed you can access the files.. for sure.
If they are just your backups.. then it really doesn't matter.. just wipe the disk and sell the whole thing off as for parts only if you cannot get it repaired.