That's totally weird given you have replaced or tried pretty much everything except the motherboard, which isn't a highly likely issue anyway. Occassionally the IR receiver but you have tried that, and usually the remote but you have tried three of them

Just wondering why with all the spares you have up there why you can't "mix and match" between them all to get one working unit, or ask for assistance to help sort out the failed units. By all means go to a Fetch if that's your desire but no reason why those TiVo's are not still fully repairable. As always happy to assist via email.