Lenovo Ideapad laptop doesn't start

Hi!

I have a Lenovo Ideapad Z565 laptop. When not using it, I usually leave it in sleep mode. For a long time it's had problems with coming back from sleep mode; when opening the lid, the fan and indicators would start, but not the screen. I've often had to try bringing it back several times before it worked.
This time, it would not come back at all. So I shut it down by pressing down the power button. And since then, when trying to start it, the following happens:
- power indicator is on
- the screen is completely off
- the fan isn't on, but there's some noise
- DVD drive makes a sound
- HDD indicator is off
- can't enter boot menu

What I've tried so far:
- connecting an external display - still nothing
- tried turning on after disassembling/assembling battery, RAM, HDD and with/without each - no result
- checked battery and AC/DC adapter with a multimeter and they seem to work
- inserted the HDD into another laptop - works

Is there anything else I can try before giving up? :(