If there is no beep confirming boot success (most systems issue one, and there appears to be a beeper adjacent to the CMOS backup battery), then most likely the PSU is turning on and things like fan(s) and probably hard drive are running, but the system is not actually managing to boot. If this is the situation, then some hardware diagnosis will be needed. If you feel confident trying this (as you've already mentioned opening the case, cleaning & checking), remember to ground yourself by touching the metal computer case to discharge static potential before handling any components in the case.
My first suggestion for something simple to try would be to see if clearing the CMOS memory has any effect. Occasionally the CMOS memory can be corrupted by some random event like a static discharge, and it sets an unbootable condition.
To clear the CMOS, with the system not powered on, move the jumper labelled CLEAR CMOS at the edge of the mainboard adjacent to the RAM slots, from its active position shorting pins 4-6 to the alternative position shorting pins 2-4 for about 10 seconds, then return it.
If the system then boots up, it may be necessary to enter the BIOS setup and select any non-default operating parameters if that system requires.
If still no boot up, the next step would normally be to see if the board can start up without any connections to any devices like drives and card reader and with the video card and memory removed. If the CPU can start, there should be continuous beeping to complain about the absence of memory. Things can then be restored one by one and booting tried again, until it's revealed which component is preventing boot up.
If the system doesn't start with just the CPU in the mainboard, that would indicate the PSU should be checked to see if a supply rail is missing or out of spec, or a mainboard/CPU fault suspected.
Edited by Platypus, 25 April 2015 - 02:56 AM.