Hi Barry
Stating the obvious then but it doens't seem to be a modem initialisation problem - sometimes the S register settings or country-specific settings in nvram can cause odd symptoms when dialling (looking for diiferent dial tones etc).
Unless it is something very obscure then I go along with Mark - it seems likely to be something to do with the s/w handling not the h/w. At least you have established that systematically and thoroughly.
I'm assuming that this modem is a 'proper' modem as it's an external one and not a winmodem It's a bit of a mystery.
Have you tried using a comms terminal program such as minicom (I think Tom also suggested this) and simply sending it AT to see if you get a response?
Best wishes and good luck! Syd