I had such a machine show up and in each case it was a different issue.
1. The power button was bad. Shorted out. Replaced it.
2. The manual for the motherboard was incorrect. They had put the HDD LED in the manual and it was actually PWR ON.

So try this. Unplug all front panel connections and see if it still does this.

Also, worth noting is a new install that powered up on its own. What was it? They had an extra mounting stud on the case, shorting out the board in just the right spot. Pull motherboard, correct the issue, rebuild.