do you have pci debug card for test ?? if you have one then check reset, clock signal for normal on it then check for normal heating of processor chip then check core voltage is good , then check for power good signal route from vrm chip also check if some code is generated on pci debug card (code only getting generated if above all things are fine), also check ps/2 keyboard num-lock state for toggle on-off led if debug card shows proper post sequencing then you have only vga signal problem try to remove small transistors near vga connector one by one. good luck.
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by the way do you have any motherboard circuit diagram having Intel h61 chip-set ??