measure all the output voltages for correct values. Perhaps attaching a load (less than the power rating of the PS obv) and measuring the voltage across the load to see if there is a significantly lower voltage drop.
Back injecting 12 volts(?) into a computer psu is not a good idea. Disconnect components before testing.
You need more than a basic experience of electronics to poke around in a computer psu, both for safety and damage reasons.
You should be aware that switched mode power supplies are inherently vulnerable to open circuit self destruction. So you should always connect some load when testing.
Computer psus have a sense signal called PS_ON which is an active low signal on the green wire on the main motherboard to psu connector. Unless this is connected to ground (one of the black wires) the psu main supplies will be held off.
Not to be a pain but here it is.
While we're at it, you can power up an ATX power supply by shorting the green wire with any black ground wire. As you know, the ATX power supply will not turn on normally without a motherboard connected to it. There are times when you may want to test an ATX power supply or use the voltage from one but don't really want to hook up a motherboard. There's only one green wire and there are plenty of ground wires so it's easy to do. To use a bent paper clip and insert one end in the green wire connector and bend it around and put it into a black wire connector. http://www.bluemax.net/techtips/ATXPowerSupplyWiring/ATXPowerSupplyWiring.htm
You might want to have a look at this thread I started on the topic of repairing SMPS.
Backfeeding 12 V before cracking the case open is foolish and pointless. All you know is the fan is working and little more.
Generally my process in the repair of a SMPS is
(1) Open case
(2) Test all output capacitors for ESR and visually. This is quick as is done in-circuit. Replace any faulty capacitors. These are the cause of many, if not most, breakdowns.
(3) Test all output diodes (generally schottky)
At this point, if the output is just the diode followed by a C-L-C pi filter then you can backfeed the same voltage and check that it holds. This should obviously not be done if there are linear regulators (like a 7805) as is often the case.
At this point we have all the secondary, output, part checked.
(4) Try to test the PS with load on the output and protection limit (like a lightbulb) on the input side. If it still does not work then the next thing to check is the (MOSFET) switching element(s). Replace as needed and test again.
(5) Lastly check the control IC and other parts on the primary side.
All tests should be done with an appropriate light load. Just jumpering the start pin is asking for trouble.
Having repaired quite a few ATX PS I can tell you that many are easily repaired with just replacing capacitors and/or diodes but some become a bitch and you end up spending way more time than its worth. It is not worth the savings but it might be worth it for the knowledge.
I agree wholeheartedly with everything GS3 has said with a couple of additions.
The Mark One Eyeball Test is the first to apply. You can often see a burnt area or exudate from dead/dying components.
Applying 12v to a fan connected to a board is worse than pointless. If the fan doesn't spin what then? Is the fan duff or shorted by a short on the circuit board?
Finally I did tell you about the green wire. Be warned further that some manufacturers, notable Dell and Compaq used non standard wiring at various times in their history. Connecting these conventionally will result in blue smoke.
If you are interested in the challenge proceed as recommended by GS3. If you are further interested in servicing pc stuff look at the link below.
If you want to test this supply and others you can by plug in supply testers very cheaply these days. These provide all the proper loads and signals and appropriate sockets and indicate function by LED.
If you want a one off test then ask a local pc shop to test it. They may well do it free in the hope of selling you a replacement.
Thanks guys I really do appreciate your insight. I am replacing the bad cap, however the only load I was able to put on it was the fan and three hard drives. I do not have access as yet to a motherboard, the two I have are in my networked computers and I dont want to use those.
Once again thank you all for your input and links.