You state you have 2.4 volts across the F2 fuse holder what voltage do you have coming into the fuse holder? If you only have 2.4 at the front side of the fuse holder then logic would suggest the problem is the connector before the fuse holder itself.

Just use your DMM to measure the voltage on the incoming wire into the fuse holder. If you have 6v to that point but on the exit lug of the fuse holder you have 2.4v then you know you have a bad fuse holder. On the other hand if you only have 2.4 volts coming into the fuse holder then you know your problem is at the other connector which could also be the problem. At this point you're narrowing down the fuse holder or the other connector where you say you're getting 6 volts into it but just because you get 6 volts into something doesn't mean you're getting 6 volts out of something. Hope that makes sense.

Exactly! What he said. You just said visually what I was trying to sputter out verbally very good.

Ok os it just me or just the pic but doesn't that f2 fuse look blackish or like it got hot?

Mouser has some real cheap shipping for small items like this so definitely check with them.