You have to find Apple Service Center, or someone can test for you. FWIW Apple Service Source manual has detailed instructions for testing, but do not even think about it, if you do not know what precautions to take.
I have replaced the capacitors on three boards of 1.25 GHz. I think you only need to replace the capacitors 1800UF 63V 8 - no 1000UF them. Capacitors 1800UF will bulging or leaking tops. Two of them can be seen by removing the cover of the memory slot on the bottom of the eMac, one on each side...
Well, there is a 56K modem that connects to a telephone line Internet access. The kit also comes with a 10/100 Base-T Ethernet that connects to a cable modem or DSL for Internet access to high speed. There is an antenna and an optional slot to support Wi-Fi card for wireless connectivity.
Well, one of my friend have little bit similar problem. He brought a broken toy with a particular problem: it worked, but after a few minutes on the front LED would flash. The LEDs are soldered by hand in the map with your child that perhaps 7 mm from the surface.
Metal SMT stencil