If the motherboard of your iMac is still functional, you can get the AirServer software, It is only $14 buck to buy, from there you can either mirror(or extend) your other Mac to the old iMac display with no mod, no wire or cable required as long as both Macs are on the same network. For $14 the AirServer is well worth buying.
IFixedIt! YEA! :) I was sad that my be loved 24" iMac went dark. I thought of all the horrible things that might happened to it. I thought the vid card was gone. I thought the backlit was gone. I thought the inverter was gone. I thought the LCD panel was gone. I open up the iMac tonight, HA! it was the backlit connector came loose! Once I snapped it back, My iMac is working perfectly, Yeeeeeeeeeaaaaaaaaah. :)))))))))))
If you want to clone the entire hard drive, here is a very good software called Carbon Copy Cloner http://www.bombich.com. It has a trial version. I like it much better then Time Machine because your cloned drive is bootable in case of emergency. :)