My Casio PX-780-M sometimes does not turn on. It has turned itself off while I have been playing it, but turned back on and operated normally the next day. It is a new keyboard less than 12 months old

SOURCE: Casio Privia keyboard PX-100

There are a number of issues that could cause this, the most likely culprit is the power supply, when I say power supply I mean the internal power supply, 
This means that you have already obtained a good "known to work" AC to DC power supply, and tested it on your keyboard to see if that is the problem. 
If you have completed this step, then your next step is to test your unit with batteries only, if the keyboard works, then you know your problem, is internal to the keyboard. 
There are two issues to check, before proceeding please read the following note.
 (a note here for those who have no experience working with internal electronics)
If you have no experience working with internal electronics I would not recommend, opening your keyboard. 
Two reasons, one, will void warranty if it still is under warranty. 
secondly, you could accidently cause more damage to the unit. 
Now if you are still reading, and feeling confident, you know that as a child you have dissembled many many electronic devices, just to see how they work. 
If you do decide to open the box, disconnect the power supply to the unit including any batteries. 
open the box and locate the power on button, clean using a Dielectric cleaning agent, can be obtained at most electronic specialty stores. 
clean the power button, may work but doubtful, usually the switch itself is usually bad, there is a way to test the switch, however, that is beyond the scope of this answer, if you are following this you will most likely have the knowledge to do this. 
The second and more challenging issue will be the internal power supply to the keyboard, or the interface that connects to your ac to dc converter. 
This can be much more trickier, and I wont go into it here. 
If you test your power switch determine that it is good then you should consider getting the unit serviced by a technician. 
If you examine the boards, (electronic circuit boards,) and notice burned, connections, (darker than other circuits) then most likely it will not be worth trying to fix. 
Hope this helps somewhat, if nothing else, take this print out to your local service dealer, and that will help in getting your keyboard repaired, 
Delete this part, before taking this to your dealer, 
Most electronic products can be easily fixed with a power switch, or power supply, however, many dealers will not tell you this and give you an estimate of fixing the unit that far exceeds the actual cost of repair, 
an example, in a local TV repair shop, a friend brought in a wide screen Plasma HD TV, quoted repair, $654.00  problem, 
power supply, actual cost, $75.00 my friend ordered the part online and with the help of a friend installed the new power supply returning his unit to full functionality. 
So beware, 

SOURCE: Casio Privia PX-120 cannot be connected to Reason or FL

When you are using midi the sounds from your keyboard aren't sent anywhere. What happens is control messages are sent over the midi cable from midi out to midi in on the other device which must have midi sounds on it (in your case the sound card) to make any sounds. The messages can be things like note on/of or pitch bend etc. If you want to send messages to produce a result on your laptop and still here something you can loop the messages by running from midi out on the device end ( your laptop) back to midi in on your keyboard. A much better explanation is available here:http://www.indiana.edu/~emusic/etext/MIDI/chapter3_MIDI.shtml I also signed up to this site (its free) that has great people and lots of info:http://www.recordingreview.com/ I recommend downloading Killer Home Recording setting up which at this time is also free and has the best advice you could want in it. I'd also recommend checking out Reaper which is comparable to Reason, Cubase or Protools. If this helps please let me know.

SOURCE: Casio Privia PX-800: When using the sustain

Check if the cble frm the pedal MIGHT be flexing or pulling on the keyboard case when you use it. Such movement COULD vibrate the power connector causing your problem.

Make sure you have the right power supply for the unit as one with too large a hole for the power pin would be intermittent like this.

SOURCE: Casio Privia PX-130, 8 months old: fluttering sound

If I were to venture an educated guess I would vote for failing filter caps in the power supply.

The power is likely collapsing under load of the speakers but headphones take much less drive.

If this has an external wall-wart power supply, you might try a new one IF the output is found to be under the rated voltage.

Internal power supply components are beyond those individuals that are not adept at electronics.

SOURCE: My Casio Px 330 keyboard

This is a problem with one of the two contacts for that key. The contacts close at different times as the key is depressed and the time it takes between is measured as velocity which is used to control the loudness as in a regular piano. The contacts are conductive rubber pills. After a lot of dis-assembly you can clean them with 99% isoprphyl alcohol and Q Tips. Clean both the pills and the circuit traces on the board they are pressed against. Be very careful of the ribbon cables between the halves of the case.