That's the expensive way!
I have a small bag of telephone plugs (US jack to UK/BT, German, French, and a few others) plus a US-jack-to-croc-clips device and a small screwdriver. I've never yet failed to make connection to the hotel telephone system, although most hotels I've used recently have a suitable modem socket anyway.
Then, I start MaGlobe, tell it what country I'm in, and the town. Sometimes it asks me the phone number of the hotel (to get the best "local area" charge rate). It asks the code for an outside line, and whether I want to use "Freefone" or "Local call". Then it connects me to the Internet. Never fails!
OK, it's 56k at best, and sometimes down around 28k8, but I can do my mail and check important stuff.
I have a separate identity on my laptop for sending via Maglobe - it uses the same e-mail address, but a different SMTP server and identification setup. That's with Thunderbird - I don't know if the Microsoft mailer packages can do that.
The Freefone bit usually means the hotel system makes no charge at all. Hotels that charge for calling a freefone number from the room are not likely to get my business anyway - that's just too cheeky!