Things you can check are;
Is the graphics card seated fully in the slot, is it a pci or agp? They can ease out if there is a bit of vibration.
Re-seat the ram in it's slot or slots.
Check all the electrical connectors to the H\D and C\droms.
Check the psu connector to the motherboard.
Check the fuse in the mains lead, the one feeding the computer.
Take the sides of the case and switch on. Does the psu fan spin up or move just a little? If it moves just a fraction and stops. It may well be the psu.