May as well try to replace them but unless one of them is for power I doubt dead caps is the reason. People love to point at caps when in reality they're not the scapegoat people want them to be. Unless it's a SegaCD or GameGear in which case that's almost always why they won't turn on.

I'd start by probing the power supply and verify it's pushing out the correct voltages and there isn't a short or blown fuse somewhere. Then probe the motherboard to see if everything is getting power.