So a broken DVD drive means that the Wii can't boot to the System Menu normally? If you can get to the System Menu through Priiloader, there are several USB loaders you can try. They all require some version of cIOS 249, though.
Hardware: Wii (PAL)
Hardware configuration: System Menu 4.1E, Priiloader
Swiss boot method: Modified Wii Swiss Booter provided by Extrems
Software medium: Retail discs