Before replacing the caps be sure the top box power supply is good. If you can borrow the one from another machine I would try that. It looks like the fan is functional and there should be a few red LEDs lit on the motherboard.
If that doesn't work carefully reseat all of the plugs going to the motherboard.
If you can swap the mpu chip under the fan and heat sink with a working one I would try that.
Replacing the caps is a tedious job and there are a lot of them. The board is two sided so it makes the job that much harder.
If you have tried all above and still no beep, capping may be the last option.
Remember this is a 20 year old computer and everything will be brittle.
Snap a few more pictures of all areas of the motherboard and maybe we can see something out of place.