I'm not familiar with the unit you're trying to troubleshoot, to be frank I've only been a pool owner for a month, but I'll try to walk you through some basic/universal electronics troubleshooting the best I can.
One of the biggest lessons I learned young, is always start simple. That led into the next lesson that a lot of failures have simple causes and simple solutions. It's easy to go too deep and skip over the problem entirely. That said, you'll need to take everything I say with regards to your specific unit with a grain of salt since I've never seen one before. You state you have power between the units, but the power indicator (LED?) is not turning on. That indicates you probably have high voltage (110V/220VAC) but no low voltage (5VDC, maybe?). Since electricity has to make a full round trip to do any work, we're looking for any potential break in the loop. The fuses provide a link in that chain that can easily be broken. A word of caution though, fuses don't blow for no reason - if you find a blown fuse, and replacing it doesn't fix the problem (e.g. it blows again), there's additional troubles to be found. But, lets start there. Grab a multimeter, and set it for continuity. Most will have a mode where touching the probes (and completing the loop through the meter) causes it to beep. If we then touch the leads to either side of the fuse and it beeps, the fuse is good. Check all the fuses. If they all test good, you may need to remove the fuse from its holder and test to make sure. If the fuse is protecting a transformer for example, it may still beep.
If none of the fuses are blown, it's time to move to the next item but for that I'd need a look inside at what you're seeing. If you can post a photo or two I can try to help. We can check connections, and if those look good we can move to trying to identify the various sections of the unit and try to see if the power supplies are doing what they're supposed to.