Greetings,
We have zero history about this system (v1 or v1.3). Did it ever work previously? Have you changed anything, upgraded a component? Flashed BIOS? H55 was released Q1 of 2010.
Thanks for letting us know you tried with a different PSU. I suspect you get no POST beep(s)? Have you tried to CLR_CMOS? Jumper is next to SATA ports. Turn off, disconnect power, place jumper over PINs. I'd pull the battery as well.
If 2 sticks of RAM, install into blue slots DDR3_1 & DDR3_3. If using USB mouse and keyboard, please connect to ports next to PS/2. Please include your complete system specs. No need to go further until you've replied with more info.