Both antenna wires are just what they appear... antenna wires. The smaller one is for an antenna that's laminated to the rear windshield. The larger one is for the powered antenna.
Check the Radio and Dome fuses. Here's the wiring diagram for the stock radio:
http://www.cygnusx1.net/Supra/Librar...x?S=Main&P=134
And here's the diagram for the stock stereo w/CD player and amp:
http://www.cygnusx1.net/Supra/Librar...x?S=Main&P=132
If you're car has the amp you may need to remove that to get everything working properly, but I'm pretty sure the new head unit should still power up.