My old iMac damaged beyond repair can I transfer all data to a new iMac???

very easy with TimeMachine.

When you have a new iMac it will have Yosemite on it.

When your old iMac is having an old OS (like (snow)Leopard or older), it is best todo a clean install. Do not use Migration Assistant then.

a. Connect the old to the new by cable, and set the old mac in target disk mode (SystemPreferences->StartupDisk).

I understand that you do have the screen black, perhaps connecting another screen works. If not:

b. take the disk out of the iMac, and connect it with a sata->usb cable to the new iMac.

You can easily boot the bad iMac in Target Disk Mode by simply holding down the "T" key when you power it on.