That last is a big clue. For background, a few facts.
All fan headers have an important secondary function: they monitor the fan speed signal coming back and detect NO signal as a fan FAILURE. This triggers an on-screen warning so you know and can fix. MOST CPU_FAN headers do much more. IF they detect no speed signal, they will warn you and then, within a short time, may completely shut down your system without even waiting for the temp sensor inside the CPU to detect high temps. Thereafter if they fail to find a speed signal at an attempted start-up they will NOT allow anything to proceed - you see a "dead machine". This sounds a lot like what you describe.
How this all works in a system with a liquid-cooling set-up depends a lot on the details of the system and WHERE the components are plugged in. It may depend also on some details of how those fan headers are configured in BIOS Setup. So to help we need as many details as you can find like this:
Maker and model of the AIO (liquid cooling) system
Maker and model of your mobo
Where is the cable from the PUMP plugged in? Does that pump have more than ONE cable? Where do those others go?
Where is the cable to the RAD FANS plugged in? Often there is more than one such, so there may be a SPLITTER or perhaps a FAN HUB involved.
When you push the front power button while watching carefully, WHAT fan are you looking at when you say it does nothing?
You say the front fan starts up, but nothing else. Does it keep running? Are there any indicator lights on the mobo showing?