How can I get internet service for my desktop without having to have a phone line connected?

You can get naked DSL, but your provider has to offer that Another option may be an EVDO card or USB modem with and unlimited (or manageable limited) data plan.

The cheap internet would be dial-up from the phone company. DSL which is faster and more expensive requires a phone line. The only two ways would be cable and Satellite. Both the Satellite and cable are more expensive then DSL. Check with your local cable provider.

You can go for Reliance/Tata Indicom data cards if you don't want a landline connection....you'll get a USB modem containing SIM of the respective company..which gets connected to the internet instantly..these are typically used with laptops ..but can also be used with a desktop..this might prove to be expensive as it costs around Rs.2400 and usage charges extra... Else u can go for a broadband connection provided by BSNL (all India)or MTNL(Delhi/Mumbai), their plans are starting from Rs.99/month + Modem Rent Rs.50/month. Their services is really reliable and connection is faster. But a landline connection is a must. Airtel also provides broadband but quality of service and charges doesn't match the former.