When a system is stored for that length of time, several things can occur. Depending upon where it was stored, moisture could have slightly corroded connectors/contacts causing poor connection(s). If the system was stored where temperatures get extremely high, an attic for example, components in the power supply, on the system board or on expansion cards could have been permenantly damaged by the heat.
I'd start by inspecting and re-seating all connections:
1. Unplug system.
2. Disconnect all peripherals except keyboard, mouse & monitor.
3. Inspect and re-seat all cable connections, memory modules, adapter cards, etc.
If the problem was a slightly corroded connection, the system should startup now.
If the problem still exists, a component may have failed.
1. Remove all adapter cards, including video adapter if your system also has an integrated video adapter.
2. Unplug power & signal cables from Floppy/CD/DVD drives.
3. If you have multiple hard drives installed, unplug power & signal cables from all but the boot drive.
4. Plug display into integrated video adapter, if applicable (see above).
Now, you should have the minimum hardware connected to boot-up.
If the system starts up, one of the removed devices must be the culprit. Re-install each device, one at a time until you find the one that causes the failure.
If the system still doesn't boot you have eliminated everything but the Power Supply, Memory module(s), System board and Hard drive.
If you have more than one memory module installed, try starting the system first with one, then the other to determine if one of them is causing the failure. If a system doesn't start with either one installed, then the failure is probably not the memory. In this case you are left with the Power Supply, System (mother) board, and hard drive.
You could connect the boot drive to another system (if you have one available) as an additional drive to see if you can access/read from it. If so, you're left with the Power Supply or System board.
It can be difficult to test the power supply without the proper test equipment, possibly a local computer shop would be willing to check it out for you. Power supplies aren't too expensive, but if it tests OK, the only thing left is the system board and probably not worth replacing on a system that's been out of circulation for 3 or more years.
I think you get the idea...