I am looking for a cheap way to get +24V DC max 3A from computer power supply. I prefer easy soldering solution like DIP, and standard components that do not need to be purchased over internet. Any ideas, please?
I am not sure you can get 3A out of it, but there are both +12V and -12V leads in ATX. You have -12V on blue wire, 0V on black, and +12V on yellow. So it's 24V betweeen blue and yellow.
If you need +24V from black wires, you'll have to arrange a boost converter and draw about 6A from the 12V. You'll likely want to use more than one lead then.
I have done this in the past using 2 supplies in series. The ground for the supply is the wall ground so to make it work I had to take one of the supplies apart and mount the board on nylon bolts to isolate it from the case. Then that supply floats and can be put in series. Not quite sure what happens around the current limit of the supply.
You can open the supply and look for the TL431 chip. There will be two resistors forming a voltage divider from the 5V rail to the 2.5V that the TL431 compares against. If you calculate the right resistor values, you can set this divider to output half the voltage it currently does. Then you can get the output up so that the +5V rail becomes +10V and the +12V rail becomes +24V. You will probably need to install new output filter capacitors of higher voltage rating as well. And if you modify an ATX supply this way, please cut off the ATX connector and install something else, so it won't plug in to a motherboard.
http://cdn.makezine.com/uploads/2014/04/da87333a_atx24-1bcq.jpg The blue wire is -12v, as @Yann Vernier said. Computer PSU, even the oldest one is a switching power supply, has no 7912 or anything like that, should handle 3 amps. I had a PSU from old computer that has 29 amps on +12v rail and 19 amps on -12 v rail.
Another way can be modifing the -12 volt rail: If you see the schematich of the power supply, you can see that there is not difference between the +12 Volt rail and the -12 Volt rail, except the rectifiers diodes and the electrolitic capacitor in the output. If you get the rectifiers diodes (from another PC power supply) you can put in the -12 Volt the rectifiers of high current, in this wa, if you use -12 to +12 rail you will get 24 Volts with 7 Amps at least if the +12 Volts is specified with 15 A