Why does it work on one and not another?

I have a mail form - 2 actually - which work perfectly fine on my host dreamhost but do not work on my client’s host which is a local hosting company, obviously he isnt best pleased.
I asked him to contact his host who says that they support php yet it still doesnt work, the mail just doesnt send.
i stress that its exactly the same script and html used to test on both hosts…

has anyone any suggestions as to whats going on??
asap would be great!!

thanks in advance!