Assuming that you have the 540 mini tower and not the 540s compact Slimline version.
Try Removing the power cord, disconnect all the peripherals, except for the monitor, mouse and keyboard. Hold the power button in, for one+ minute to release any residue power from the motherboard. Reconnect the power cord to a different outlet without the surge protector and power the 540 on and see if this makes a difference.
The Studio 540 Troubleshooter is HERE
As the power button LED is not lite and no beeps, it could be a possible power supply, or motherboard issue.
The only 100% method of testing a power supply, is to install a known working unit and this would cost less than a motherboard, suggest that the power supply is the first part to be replaced.
Most generic standard ATX power supply units, with either a 24-pin or 20+4-pin main motherboard power connector, with or without the on/off switch.
You should be able to buy a compatible power supply from either a local or online computer store.
Note: You require a power supply with four SATA power connectors.