Show me someone who hasn't had a problem with hotel switchboards and I'll show you someone who has never tried to log on thru a hotel switchboard ...
A couple of things I have learnt along the way ... Hotel switchboards are sometimes very slow to switch from the internal dial tone to the external dial tone (maybe they need time to wind up the egg timer or something). Solution is to add one (or more) commas between the number you dial for an outside line and the external number you are dialling. These act as pauses in the dialling process.
Another problem can be the frequency of the external dial tone - sometimes your modem will not detect the dial tone - and waits for ever before dialling. Solution is to uncheck the "wait for dial tone" option in your modem set up.
Some older PABX's incorporated a "low pass" filter in the speech circuit (to improve speech response). Not very common these days but I have come across it in the past. This can lead to multiple retries and dropped lines. Solution is to cut your speed right down - try 19 200 baud or even 9 600 baud. And yes, you're right, this sucks if you're trying to browse the web, but is just about tolerable to download e-mail.
Digital phone systems will indeed blow the !!!!! out of a conventional (analogue) modem. And no easy way to check - except call the hotel switchboard and ask whether they have a digital phone system. If it is a digital system, the only solution is to use one of those gizmoes that straps onto the handset (aka an "Acoustical Coupler"). Rather quaint but they do work. Or failing all else, ask to use a FAX line (they are always analogue).
There is a s/w package from Norton (or Symantec) called "Mobile Essentials" which looks like it could be helpful (I have actually got a copy somewhere but have never used it in anger). Has diagnostics that show you where the problem is - not very expensive - might be worth looking at if you absolutely need to get connected.
Hope that helps - and good luck (my experience is that you need plenty of that!)
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Feline
(I Sit, I Watch, I Smile)