Dead Apple //c ?

Welcome to the forums!

Do you have a volt meter?

Any time you have a power issue like that (on any electronic), with a good PSU, my first suspect is a failed voltage regulator.  Earlier //c motherboard revisions use a 7905 (later ones used something else that I have yet to identify).   A new 7905 will cost about $1.50 (plus shipping if you order online).  The regulator is marked on the motherboard near the inner front corner of the internal PSU and looks like a little black square laying on its back with three prongs soldered to the board, with a metal heat sync bolted to the board on the other end (the pins face towards the front).  You'll want to check the voltage on pin 3 (the one on the right).  For further testing the pinout is as follows: 1) Left, Ground/Common, 2) Center, Unregulated + Input, 3) Right, Regulated -5v Output.

I would start by looking for any signs of physical damage.  This can appear as discoloration or corrosion on the pins.  If you don't see any then I would test it with a multimeter for the correct voltages.  Important note, this test needs to be done with the external PSU plugged in and the computer switched on, so whatever you do, be sure not to touch any two pins with your probe at the same time, as this will cause a short that can damage other components!

In any case, while there are other possibilities (corroded pins, bad capacitors, blown fuses, ect.), the odds are this is a simple and cheap fix.

To test the voltages on a 7905, you'll need to set your multimeter to 20 on the DC volts side (as seen in the picture below). With the red probe, touch pin 3, and the black probe touch pin 2.  be careful not to touch the two together or touch pin 1 with the black probe, as this will cause a short that can damage other components.  If the 7905 is working, then you should get a reading between -4.8 and -5.2 v from the red probe on pin 3.  (Note: This reading should not fluctuate.  If it is, then your 7905 is failing, replace it)  If the reading is positive, then likely you have your probes crossed (negative and positive refer to the current, not specific values), just make sure the black probe is plugged into common, and the red probe is plugged into the spot marked VΩmA, then try again.  If you get a reading above the range mentioned,  then the regulator has failed and needs to be replaced.  Turn off your machine immediately, as the higher voltage can damage other components.  If you don't get a reading at all, or the reading is below the stated range, then move the red probe to pin 1, careful not to touch the black probe or touch pin 3.  I believe that the reading should be between -9 and -14 volts, but anything above -5 volts should work.  The readings will likely fluctuate, which is normal, as pin 1 is unregulated.  If you get no readings or readings -5 volts or below on pin 1, then power isn't reaching the regulator.  This would indicate a corroded contact, failing capacitor, an open on the line (broken circuit), or an issue an undiagnosed issue with the PSU.  If you do get good readings from pin 1, but not pin 3, then the 7905 has failed, and again it needs to be replaced.  If the 7905 checks out, then your problem is further down the line.

Multimeter 20 DC.jpg

From the picture you posted, your board looks pretty much pristine.  Even the 7905 looks good, but if you're not getting any readings off it, even on the input lin, then my suspicion is an issue with the external PSU (given that you've replaced the internal one already).  To test this, you'll need your multimeter again, set to the same settings as before, and two to four paper clips or pieces of wire.  With the brick plugged into the wall hold the plug that goes to the //c facing you with the notch turned down.  There should be 7 slots or holes on the end.  Bend out one end of the paperclips and stick one clip in each of the holes to the left and right of the center (note: you don't have to do all four at once, just one on each side).  Place the red probe on the clip to your left, and the black on the clip to your right, then use the multimeter to measure the voltages between the two clips.  On a working PSU, you should get somewhere between +9 and +20 volts on each left clip.  If that's what you get, then remove the clips from the left holes, and stick one into each of the two holes on the right, and set your multimeter to continuity mode (the little speaker icon), for a ground test.  Touch each clip with the probes (doesn't matter which clip or probe, as long as it's one probe to a clip).  You should hear a high pitched beep.  

Ideally, the two holes on the left should be +15 volts (however, they are unregulated so over or under is fine as long as it's close to the range specified above), and the two on the left are ground.  If you don't get any readings on the left, then likely the fuse has blown, or some other internal component has failed.  If you test the continuity of the ground holes and get no beep, then there is an open on that end of the circuit.

The last thing you can do is plug the brick in for 5 to 10 minutes (whether or not it's plugged into your //c is immaterial since the brick draws power regardless) and see if it gets warm.  If not, then it's dead.

 While these issues can be fixable, but //c Power bricks are not user accessible (at least not without a hacksaw) and it would probably be easier to simply replace it.

I know that you already looked at your brick, but the thing about these old PSUs is that externally they can look fine, and still be screwy on the inside.

Still, if the brick does check out, then the next suggestion would be to check for a dry solder joint on the bottom of the board.  Probably around the power switch, or the 7905.