First do you see a light indicating that the TV has power? There are two power buttons on the TV (the main power and the regular power button). The red standby light will light up when the main power switch is on. This indicator is just to the left of the remote I/R sensor. You can find the main switch on the bottom front of the tv (it is under the tv forward of the stand). Turn on the Main power if it is not on. Then try the power button on the control panel of the TV again.
Does the standby light change color or blink? (Red is standby, orange is power savings (no signal), blue is on.) If the main switch is on and the standby light doesn't come on, the TV has a problem at the power supply. Try unplugging the unit for a bit (at least 30 seconds) and then plugging it back in. This will reset the internal circuitry. If you see a blinking light, then the TV is reporting a self-test failure. I do not know the codes for this model Hitachi Plasma TV.
The manual for the Hitachi P50H401 TV is available from Retrevo: http://www.retrevo.com/support/Hitachi-P50H401-TVs-manual/id/1233ci869/t/2/
. You will need to enter a code to access the pdf.
I'm assuming you don't have one of the special versions that were intended for large audiences that were only controlled by remote (no control keys on the front of the TV). Remotes.com has the original remote or a substitute remote if you need it. See http://www.remotes.com/remotes/servlet/rs?a=gmi&uuid=13104063628240&smodel=P50H401&brand_pn=HITACHI_P50H401
I hope this helps.