The psu may have a active power switching. Give it a try on 110v also what's its model?

Wile not necessarily required. I'd unplugged the psu from the system and ground the green wire form the motherboard.

That all aside I'd go for a newer 450w psu in a p4 system.

If 110V applied to 240V Supply, shouldnt it simply not work in baddest case ?

Doesn't matter where in the world it is from, power requirements wont change. 350w is a 350w on the PC side, its just expecting a different voltage from the wall.
That said if you want a rough idea you can find many power supply calculators on the interent
http://images10.newegg.com/BizIntell/tool/psu … tage-Calculator

PS
Never done it the other way round but I know from experience that supplying 240 to a 110v power supply kills it, and again 5 years later, same result! 😊