Again - to the best of my knowledge, there is no way to "dial-up" a DSL line. DSL is something that has to be PHYSICALLY wired to the phone line in question - NOT a service that you can simply access on demand. DSL is based on a DSLAM being physically connected to your phone line at your phone company's Central Office. Chances are, this hotel has a local PBX, which accesses a fixed number of outside trunk lines with the local telco - when you press '9'. That said, you're even further removed from the possibility of DSL access as your PBX would ALSO have to provide DSL access.
Unfortunately - dialup is really the best you're going to do.
Here are a few thoughts you may want to consider:
1) Does this PC have WiFi access? If so, you may want to scan for WiFi hotspots near your hotel. Many cafe's offer free WiFi access - so if you're near one and have WiFi capability, you may be able to snag an Internet connection that's faster than dialup.
2) All of the big, national cellular carriers (i.e. AT&T, Sprint, Verizon, etc) offer wireless broadband services in most major metropolitan areas. I've not done pricing on this - but I suspect that the plans are somewhat pricey. Anyways - you can subscribe to these services and access them one of two ways 1) install a cellular modem in your laptop or 2) Connect a compatible cell phone to your PC via a USB cable - making your cell phone into a cellular broadband modem. Again - these options require you to subscribe to the wireless carrier's cellular Internet service. If the area you're in has access - you should get FASTER speeds than 56K dialup.
Hope this helps.