Yup, WoL will only work through an ethernet port, and it's not always supported. The only option I can think of is:
In BIOS there is usually a setting on what to do after power loss, stay off and turn back on are usually two of the options. Try playing with those.
...that one. There's often 3 settings as to what to do after recovering from power loss, off, last state and on (or words to that effect). If you switch it to on, then it *should* power on whenever you give it power - hopefully!
Failing that I think you'll have to just mod it