Generally speaking, I believe there are 4 ways to access the internet via your Axim.
1) Using your PCs internet connection by passing-through the PC via an ActiveSync Session using the sync Cradle/Cable. Obviously this has the least amount of "mobility" but no additional hardware is needed.
2) Wireless through your wireless network or wireless sync session using your network's internet connection. A little more mobility but must be in range of your Wireless Access Point. Obviously you must have access to a wireless network and have a WiFi CF card for your Axim.
3) Through a wired dial-up connection. Need access to a wired phone line. Requires a CF-modem card for your Axim.
4) Through a dial-up connection (using your cell phone). Can be used anywhere you are in range of your cellular service. Other than the cable to connect your Axim and cell phone, no other hardware is needed. Here is the link to a web site with more info.
http://store.yahoo.com/gomadic-new/delaxx5adtom.html
To use either of the last two options you must have an ISP that supports dial-up connection (I know you mentioned you currently connect via cable modem). In the last option, your cellular service provider must support data transmission (I think most do).