a 20pin power cable will not power a 24pin motherboard.
and if you mean the 8pin CPU power, this is also necessary on majority of modern boards.
you will need to include your complete system specs for both the old build and the new motherboard plus any other new components you are planning.
if this is a power supply from an old HP/Dell/Compaq desktop then i seriously doubt it can work or will even offer enough power for an average custom build.