Computer won't start up - stuck on Lenovo splash screen

Visual inspection:

1. First remove mains from power supply and after that press power button once.
2. Remove covers.
3. Check if there is a dust in radiators or fans. Clean with compressed air if needed.
4. Take visual inspection, focus on capasitors at motherboard and check if any of them is broken / leaking / blown. Here is another answer with picture.
5. Check that all radiators are firmly attached in place.

Results and going forward:

Visual inspection: Dust it is possible that components under clogged radiators may have been overheated and possibly broken. Testing single components is not so straightforward and requires either known good components around them or special testing equipment.
Visual inspection: Capasitors If you have problems with motherboard capasitors you should replace your motherboard, you can also attempt to replace capasitors with new ones (make sure they have same ratings).

After visual inspection comes basic testing:

Find out if it works as expected with minimal system configuration.

To perform this basic test you should disconnect everything that is not essential for booting up operating system. Basically this means disconnecting hard drives, optical drives, front panel USB/other connectors, any add-in cards and all but single RAM modules.

After you have done this try to power up your computer, it should load BIOS and complain about "Operating System not found". If it still hangs, swap memory modules still leaving only one module in and retry booting. You could also try selecting different memory bank, not first one.

If this does not take you any further then you should try to reset BIOS. There could be switch or button for that labeled "CMOS reset" or something similar. Another way to reset BIOS is to take off battery that is located somewhere in motherboard and pushing power button for 30 seconds without mains connected.

After that, try to power up computer again with minimal system configuration.

Results and going forward:

Boot process goes further: this basically means that you have removed faulty component, this raises up quoestion about which one it is? Start by connecting hard drive again and after that try to boot up. If it works, take all other components but RAM, put them back and try to boot up. If it still works connect everything, try to boot up. If it hangs remove RAMs, download memtest86 and test all RAM modules with it, one by one. You can also test your hard disk with SeaGate Seatools (drive can be from any mfg).
Still hangs at same point: Notify about it here at comments and we can try to make some deeper inspection.