What would you use to "waterproof" a gutter? (Home Depot was clueless)

Ok,

I'm a greenie and still learning with all things house-repair.

We had a flat roof re-done over the garage to stop some leaks but now have this weird leak coming from what we now believe to be the gutters.

Basically, you know how there is this 4-5" 'rod' that goes from one side of the gutter to the other and is attached to the wood using this nail/bolt from the outside, through this hollow rod, and into the structure.

Problem:
What we think is happening is that as water drains off the re-done roof and into the gutter, it's sliding down the side of the inside gutter wall and water is making it through where the gutter is attached to the roof (via that rod/hole).

Q: What can I apply to such areas to waterproof it from letting any water out?

It's dirty and I can't easily clean around the attached portion so what can I apply? Is there something special or do I just put a bunch of silicone and hope it adheres to enough and prevents water from taking the path of least resistance?

Thanks in advance!

 

If you do not mind the holes in the front side of the gutter, I would replace the old rod and nail system with the newer style gutter clips that are mounted inside the gutter. You would remove the old and install the new clips one at a time. Fill the hole left by the old nail with silicone caulk and screw the new clip in just slightly to the side of the old hole. The wide base on the new clip should cover the old hole. The old nails are probably loose and the new would not hold if you put them in the same place. But you need to screw the new into the rafter ends therefore you need to be close to where the old were. That is thinking the old were nailed properly into the rafter ends.