I'm going to proclaim my ignorance here, and my blue book is on loan to a Seattle member. Fused power leaves the cabin and enters the engine bay. You shouldn't have relayed power heading back to the fuse box - it defeats the point of having relays. So to answer your initial question, your fuse box issue isn't a relay issue. They are mutually exclusive. One or the other could be a problem though. I suspect that the fuse box is fine, and you just didn't test something right down there. By "power probe" I presume that you mean a multimeter. By "signal lights", I presume that you mean parking lights and not turn signals.
As far as the engine bay goes, I would ultimately ditch all of that poorly executed nonsense with the two aftermarket relays. I would go back to factory for now. Understand wiring in the process. If you want good night driving, rewire again with new relays and wire. I don't think those are fog relays. I think what you have is a supplemental low beam relay and a high beam relay. It should be easy to figure out, but I will come back to that.
Real quick, here is how relays work. You have constant power from the battery. The relay is grounded as well. You have a signal wire that comes from some power source in the cabin. In this case from the HL switch. This closes the relay, like one of those big lever switches in the Frankenstein movies. Once that relay is closed, it sends full power to the device. The advantage is that you have low current signaling the relay to engage, and full power from the battery to directly to your device. It prevents you from having to run your headlight power through old HL switch wiring. They just need to have enough juice to power the relay. Make sense?
Low Beam:
Using Chris's info, find the yellow low beam wire. A real yellow wire not yellow electrical tape. Also not the super shiny new yellow wire going into the low beam terminal on your H4 bulb socket. With the ignition on, test power to the output of this wire. Hook the red lead on your multi-meter up to the old yellow wire, and ground to the body or the negative terminal. The question is - where is the yellow wire. I suspect that it is going directly into 86 (the signal wire) on one of those two black relays. Here is the deal for your aftermarket low beam relay:
Pin 30 - Inside that giant yellow bundle, wired directly to your positive battery cable
Pin 85 - This is going to ground, probably near your battery or on the negative terminal
Pin 86 - This should be your old yellow low beam wire, or perhaps a pig tail that goes back to the original wire. This is the wire that should get power with your headlights on, and your highs off
Pin 87 - This is a full 12v going from your black relay to the shiny new yellow wire on your H4 bulb socket
Rule out this relay, just check that you are getting power from the old yellow wire. Again check pin 86 on the black relays. If 86 is receving a signal, the black relay is probably bad. If they aren't actually physically secured to something they will go bad faster.
High Beam:
Using Chris's info, find the high beam wire. Start with the high beam can relay. I don't know what color it is going into the relay, but it will go into Pin 86 (again, the signal wire). Listen for the click like Chris mentioned. If no click, you can pull the relay and use the multimeter. Red on the 86 terminal and black on ground. The next step is to see if they added a *second aftermarket relay after the factory high beam relay. If that was the case, the can relay pin 87 would be sending power to 86 (signal wire) on the *other black relay. If the can relay has nothing to do with that second relay, that second black relay is probably a fog relay. Another easy test to determine if that black relay is a high beam relay is to follow the shiny new green high beam wire on your H4 bulb socket. Does it go back directly to the can relay or does it go to to the black relay? If it goes to the black relay than you have a redundant second high beam relay. If it goes directly to the can, then the second black relay isn't for the high beam.
Testing Results:
If you aren't getting power to your factory HL wires, you probably have a problem with your HL switch, and possibly your high beam switch. If you are getting power in the engine bay, it is that bird's nest of supplemental relays.