Sounds more like a bad ignition switch or starter circuit wiring issues....not likely a coil issue....since the radio has no power either. A coil issue would not affect the radio. Check for blown fuses too.
The starter relay has a couple yellow wires on one terminal ....one of which powers the ignition switch circuit for the starter. In that wiring is a fusible link wire which may be bad too.
Fusible link wire looks like regular wire but internally, it is 4 gauge sizes smaller to act as a slow blow fuse and protect the circuit wiring from frying due to a short or overload. So if the circuit uses 14 gauge wire, the fusible link wire will be 18 gauge.
I'd test the yellow wire that runs from the starter relay to the ignition switch to check for good power. If you get power at the relay but not at the ignition switch, then the fusible link wire may be blown. Look for signs of melting or arcing on the wire sheathing near the relay. Parts stores sell fusible link wire in various gauge sizes..cut out the old one which is likely spliced into the yellow wire at the relay terminal and take it along to match up for same size and length. Usually, there are markings on the sheathing of the fusible link wire which gives a gauge size or ohm rating of resistance value. Then splice the new fusible link wire in place of the old one with new terminals/connectors...check the circuit for any shorts to ground...frayed wiring, corroded connections ,etc..
If you do get power at the ignition switch yellow wire, then check for power at the red/light blue stripe wire at the switch which carries power to the neutral safety switch and then onto the starter relay to operate the starter. A white wire spliced into the red/light blue also powers the ignition module.
Could also be a bad or misaligned neutral safety switch. You can jumper a small piece of wire or paperclip across the two terminals at the neutral safety switch wiring harness to bypass it for testing...if it starts with the jumper wire installed, then the NS switch is bad .
Wiring diagrams ...
http://arrc.ebscohost.com/statics/p5/images/sm/isbn_graphics_complete/8667/chiltonimages/8667/86676e15l.jpg