tweetie7777,
According the to FAQ that I linked to (the second one), you can't directly suppress the Print dialog unless you're using IE4. In IE5, printing is considered a security risk and therefore must be confirmed. (This is their story, not mine.)
Later in the document, yhey do refer to some additional alternatives and include some C code that shows a few different tricks. It should be possible to use the same tricks in Delphi, but I'd review the source for the TWebBrowser component to make sure of the datatypes and so forth. (If you have Professional or Enterprise versions of Delphi, you can find the source in \Source\Internet\shdocvw.pas.)
I haven't tried these out, so I don't have a specific answer, but worse comes to worse, you could determine the class name of the Print dialog and then use a timer that calls FindWindow() to get the window handle and then send a message accepting that window. That's a very crude thing, something I'd probably try as a last resort. But, it should work if nothing else does.
Hope this helps...
-- Lance