Do you know why you're not able to get ADSL? Have Telstra (bigpond), or anyone else for that matter, given you an explination?
As for avoiding Telstra's lines and using ADSL, there's simply no way around it. Telstra own the telephone (pstn) line infrastructure. ALl providers must use these lines for adsl services in some way or another.
Naked DSL is an option. This type of ADSL means internet providers have to pay a fee to telstra to 'hire' their telephone lines from them. By doing this you can do away with the need to pay a monthly fee for a phone service. The naked dsl provider includes this small fee into your naked dsl service. iiNet and Internode are currently offering these services with ADSL2+ speeds.
Other than this option, you could try give Optus a call and see what adsl/cable services they can offer you.