We have had the radium track lighting for many years. It recently stopped working so we thought it was the dimmer switch. It is not the dimmer switch. So we looked at the lights and they aren't burned out so that leaves the transformer. We would like to purchase just another transformer but don't know how. It reads: Anchorn model #AET-D1051 input 120v 50/60hz output 12v 105W/max. It does not appear that any of the wires are melted but we can't think of any other solution.

First check present transformer using a multimeter. Input side should read 120v. Output side should read 12v. If you have input voltage and no output voltage transformer is defective.
Google "Anchorn model #AET-D1051".

Order new transformer $8.80

105 watt 12VAC Electronic Encapsulated Transformer MDL 316-0004 (http://www.totaltransformers.com/105-watt-12v-ac-electronic-encapsulated-transformer.html)