Computer shut off and on by child & now wont boot?

does it power up?

wait nm if it smells like its burning you got issues man i wouldn't run power to it through that preticular power supply anymore and you may want to pop it open and check the motherboard make sure there is no burn spots and that the capacitors are not popped

Before possibly mucking anything up, i would strongly advise you to take it to a local computer repair shop, in the least they should be able to recover your data for you.

Data recovery is extremely easy to do. Repairing a dead drive however is extremely costly and usually not worth it. The line where you said "I tried my sata hard drive in another computer so I could at least recover my pictures. It wont boot and it says there is no image on the drive!" Are you trying to use it as a boot drive? if so that will not work at all you have to set it up as a secondary drive and go into windows on that pcs boot drive.

I would try a known good power supply and do this in order.
1: unhook the current psu
2: have everything unplugged/unhooked except the bare essentials
IE 1 stick of ram, onboard video if you have it, onboard sound, no dvd drive, you could even unplug the hdd but that usually isn't an issue.
3: before plugging it back in take out the CMOS battery and leave it out for a good 20 minutes and discharge the caps on the motherboard. (do this by having holding in the power button on the front of the case. Make sure the power supply is switched off in back.)
4: only have power leads going into the 20+4pin and the atx12v connector (the 4/8pin cpu connector)
5: plug the cmos battery back in (Oh and before you take it out note which side it was in, positive or negative, I can't remember   )

Then try to turn it on. if it still doesn't boot you could try bread boarding it or heck you could just try that before hooking up the known good psu...

Usualy no boot assume power-up, but then why he changed the power supply ?
Someone who know better will try to boot with hiren`s boot cd or windows setup disk and choose repair and in that command line write "chkdsk c:" (try /p or /f option).
In your case i would not recommand it since you are more than parallel with computer hardware (based on your own description of problem)!

In the future backup your files. There is a saying that that on the the Internet that goes somewhat like this: "if a there is only one copy of a file, it must not be a very important file"

That's a misnomer meant to try to get people to backup the files they think are important.

Also it's possible the child pressed the start up and off button while you were gone and broke something  
don't be too mad thou

But on a solid computer, with a well made PSU, that shouldn't have broken anything regardless (maybe the button that starts it would have broken?). I think this sort of thing was bound to happen with your computer eventually, unfortunately. The child just 'seems' to have sped up the process.

Unless it's brand new, but you did say 4 years of work, does that mean the comp is 4 years old? (or just the HDD?)

Btw your motherboard probably is fried.. When that happens everything can go boom, if the shock was enough to break the mother board it can be enough to break other parts of your computer.

I'd say take it to a repair shop as well, reputable if you can. And try to price the service, there maybe other shops that do the same/different thing(s) (and quality or work) for different prices..