If im right, there are two connectors on the rear screen normally (can someone confirm

), one will be an earth and one will be a 12v supply, make sure you have a good earth and also check you have 12v with a voltmeter or circuit tester, both can be bought from a good motor factors.
Also check each individual heating element strip on the rear screen and make sure none are broken.
Im new to bmw's aswell but these are the checks i would usally do, oh and also check the fuse!!!
Hope this helps, let me know if you need an explanation on how to check the earth and power(12v).