In your forumdisplay template find the bit that says about newthread.gif and around that code add something like:
Code:
<if condition="$bbuserinfo[userid]!=x">
all the stuff about newthread.gif
</if>
Change the x to the userid number of the user that you dont want to display the button to.
There are two instances of this in the template so make sure that you do both of them.
BTW, I've not checked the code, just done it from memory so if theres a bug give me a poke and I'll fix it.