Laptop Power Anomaly

I have a Compaq Presario V3000 laptop - I think nearly 3 years old. I am having some 'power on' issues. When I hit the power button, lights all come on, DVD drive boots, but Hard drive doesn't and I end up with just a black screen. So I hold down the power button & turn off the laptop, then hit the power button again and it boots up absolutely fine. This happens virtually every time - first time it doesn't boot, second time it does.

The above happens when I am plugged into AC power - when I try to power/boot up on battery only, lights all come on, DVD drive boots/whirls , but Hard drive doesn't. So I repeat the steps above, turn off the laptop & then power back on again, but it doesn't boot up. Then if I plug in the AC plug, turn off the laptop & power on again, it usually then boots up fine.

Before someone may suggest that my battery has gone, I have actually just replaced the battery (as the old one was on it's way out), and once I get my laptop booted (via AC power) & running, I unplug my AC plug and I get about 3hrs on battery life - so I don't believe it to be the battery. HOWEVER, my hard drive recently died & I had a new one installed and according to the technician, it booted up fine at least 30 times! Go figure!!

Would anyone have any suggestions?? I have been doing some reading on blogs & forums but have yet to find someone with a problem such as this. I know intermittant computer problems can be very hard to diagnose & solve, but this almost isn't intermittant in that it is a regular pattern of: 1st time=no boot, 2nd time=boot - but then that is only happening when I'm plugged into the power.

I've seen topics around the place to do with BIOS settings, and I have been to the HP website & done all the updates I possibly can on those kinds of things. I am at a loss to know what to do - I'm not a 'computer tech' by any stretch of the imagination, but I am trying all possible means to solve the problem myself - largely to save $$$ taking it to a repair person & because I would need to find a technician who really knows what they are doing (sadly, past experience has shown me that some "technicians" are people a bit like my brother who just like to 'fiddle' with things! LOL)

Any suggestions or direction forward for me would be HUGELY appreciated. Thanks for taking the time to read my novel!! Kind regards.