There is no really good way to test a part based on a visual inspection. If you see any damaged, disformed, or "fried" components, then the chances are, it's bad. Sometimes, though failure can happen on a non-visual level. For example, a bad solder joint (Solder holds every component to the board, and forms the electronical connection) which can be virtualy undetectable, or a bad intergrated circuit, such as damage to a chip that isn't visible on the outside. The best way to test anything it to plug it in. Note, if you are going to buy a case, keep in mind that each logic board has it's own specific case.
Logic Board Info (Based on date on board, with name, and nick-names)
1999 - The original powermac G4 (Graphite, "AGP Graphics", "Yikes!")
Early 2000 - See Above
Late 2000 - Powermac G4 Quicksilver (Digital Audio, Gigabit Ethernet, Quicksilver)
2001 - Powermac G4 Quicksilver (See Above)
2002, Green - Powermac G4 Quicksilver (See above, except includes LDS)
2002, Navy Blue - PowerMac G4 MDD (MDD)
2003, Navy Blue - PowerMac G4 MDD (MDD, some may have a firewire 800 port, as well as 2 firewire 400 ports)
2004, Navy Blue - PowerMac G4 MDD (MDD, Last PowerMac G4 Produced)