From experience of having repaired a friend's PC it may be worth investing in a new battery for the motherboard. Cost about £8 (ISTR) but the PC sprang into life after and is still working fine. It's very low voltage but it kick starts the boot process and if it is dead then it won't boot.
Oddly that is a Mesh PC as well - not sure of age to say that this is a common failure though.
Hope it helps
