Replacing the I/O board is of moderate expense and difficulty - at this point (dead machine) it's a good place to start. Buying a bunch o parts to test is expensive and time consuming.
If you can charge your battery in another machine '''you could try force starting (jumping)''' the machine bypassing top case and power button. If this fails your logic board does have damage. Finding that damage and reparing it is very advanced DIY work (you could check out prices from places that repair your logic board with a replacement board)''' Replacing the logic board is a major DIY project.''' Check out the two repair links to see what you're in for and for troubleshooting steps.
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