Welcome, Newcomer. This could mean that you have a short circuit in the power button. The power button is actually just a push button toggle. The toggle opens and closes the power switch circuit on the motherboard.
Because this is a prebuilt system, you may find that testing this theory will be difficult. However, for shits and giggles, open up your case. Trace the wiring from the power button to the motherboard. If the wires stop in a plastic connector that attaches to the motherboard, pull off the entire connector. If the wires connect straight to the motherboard, remove just the wires that connect to the toggle.
Now that the power switch pins are exposed, you can jump the pins by using a flathead screwdriver. Doing this should turn on the power to the motherboard, if not, continue reading.
The next suspect would be the Power Supply Unit, or PSU. A PSU has two basic functions:
1. To convert AC power into DC power, which is what your computer needs; and
2. To distribute DC power to connected peripheral.
The PSU typically fails at step 2. This is apparent by testing the voltages with a multimeter. Another way to test if the PSU is the problem is by swapping it out with a known working PSU.