|If the mboard has a 24 "pin" main connector socket, you usually MUST use a 24 "pn" connector from the power supply in it, or the equivalent,|
For many power supplies, there is a 4 pin connector on the same wiring bundle as the 20 pin one - if you have that you plug in BOTH of them.
They can only plug in one way, one place into the socket
If your power supply does not have that, you can probably buy a wiring adapter locally from a place that has lots of computer parts to adapt the 20 pin connector to a 24 pn socket .
(20 pin female connector to to 24 pin male connector)
A 250 watt power supply probably has enough wattage capacity if you are NOT using a video card installed in a slot,
but if you ARE using a video card installed in a slot, you may need to get a power supply with more capacity in any case - a new PS would have the proper 4 pin connector on the same wiring bundle as the 20 pin one
If you ARE using a video card installed in a slot, tell us what it is.
If it's video chipset requires that your system has a PS with a recommended minimum capacity of a lot more than 250 watts, that's another reason your computer may not boot, when the card is installed.