I'm working on an x250 with the same problem. Symptoms are keyboard lights up and goes off, CPU fan comes on for 5 seconds, solid green light on the power button and no display. No other indicators. If I press the power button for 1 second I hear a quick pop from the left speaker. Press power again and the cycle repeats itself. Removed RAM and didn't get any beep codes. Dumpped the BIOS and reprogrammed with a known good one for the 20CL, NM-A091, N10RN04W just in case but no change. Reflashed with my OEM dump and started probing. No shorts. I have 20v, 5v, 3.3v, 1.8v rails. All MOSFETS are good...

Re: No power Hp compaq Cq61

I just fixed one of these. A CQ61-420US came to me with no POST and 2 light flash code. This pointed toward corrupted BIOS. I removed the RAM and tried to power it on. Laptop produced a beep code of "Missing RAM". Installed one stick of RAM, back to 2 lights flashing twice. This tells me that there is no hardware fault since the bios is loaded enough to produce beep codes. If there's a hardware fault like a sloppy solder joint then you will never get to POST. Usually bad GPUs do this.

Anyways, I tried copying bios F15 onto a USB...