Need help identifying this fuse resistor
Look around on distributor sites for PC mount fuses.  Look particularly at the Panasonic line, since they have a series of power resistors that look almost exactly like that.

You could take the one out of the working unit, connect it to a lab power supply and slowly ramp up the current to see where it breaks.  Now you need two fuses, but at least you know the current rating.

Since this is a one-off, you don't need to find one in exactly that package.  You have a lot of room, so you can rig up most thru hole fuses to fit in there.

Another clue is the power rating of the power supply.  It is rated for 38 W out.  Let's be pessimistic and say 80% efficiency, so 48 W in.  With 110 V AC input, that would only mean 430 mA.  There will be some startup inrush, but that is short-lived and most simple fuses can ride it out.  1/2 A is cutting it close, but 1 A should be more then sufficient.

It's not that critical.  Even if the original was 1/2 A and you replace it with a 1 A fuse, nothing serious is going to happen in this one-off situation.  The most likely failure that blows a fuse is a dead short, or close to it.  Whether the fuse trips at 1/2 A or 1 A won't matter for that.  

That all said, there is a reasonable chance that replacing the fuse won't solve the problem.  It may well be that the stray wire caused something to get fried, which then caused too much input current to be drawn, which blew the fuse.  In that case, a new fuse will just blow again quickly.