The PSU should be sufficient to at least confirm it can boot. If you are ever able to do so, you should replace it with something else. Though based on your post it sounds like it was the best option out of the PSUs in the different systems.
Looking up the eMachines system info, I get this motherboard:
It looks like Socket A motherboard to me. It doesn't have any CPU power connection that I can see so that concern is not present. Thing is, the motherboard model doesn't match, so it was probably replaced, particularly since tis picture doesn't match the ones I find for the motherboard model listed, which appears to come from an HP.
In addition to the notes Dave provided-
-You only need one network card. It sounds like you grabbed as many expansion cards from the other systems and crammed them in. It might work, but it is incredibly pointless and will saturate the PCI bus. Personally I'd remove all of the added cards except for the graphics card, then add them back once you can get it powered on. You generally should start with as little as possible, then add components. You might even try only powering up the motherboard with no graphics card connected- the motherboard should give you a series of beeps indicating it couldn't find the graphics card once it powers on.
-Did you plug in the main 20-Pin power connector from the power supply to the Motherboard? Make sure that is in place. If the board is the one Dave pointed out, then you need to connect one of the molex connectors to the connector portrayed in the lower-right side of the picture.
-you mention a power switch as having a light. But you also state there is no power switch. I'm unclear what you mean. The Power-Switch is a separate front panel connector which in Dave's picture of the motherboard would likely be the set of pins in the lower right, to the left of the Molex connector myself and save pointed out. usually it will be labelled with silk-screen nearby; you'll want to connect the power switch front-panel connector to the one labelled "PWR_SW".
-The Power supply might not work at all.
Not sure how you are going to get a 500GB Hard Drive to work with this board because it only has IDE ports, and I have yet to find a 500GB IDE drive. The 500 GB drive is likely SATA in which you would need to add a SATA controller and then configure the BIOS to boot off of the SATA HDD which in some BIOS's can be a nightmare if lacking the necessary features to do so.
I have a 500GB IDE drive- WD5000AAJB, WD Caviar SE. I see a 500GB IDE drives by searching Amazon for "ATA-133". They are definitely harder to find new. From the sounds if it, the HDD was salvaged from one of the other systems and I suspect it might be old enough to also be PATA.
I think the bigger concern is that even if the HDD is IDE, and does connect to the system, the XP Install on it will be for the other system, and probably won't boot without a repair install, which typically requires an XP CD which from the sounds of it the OP does not have.
