There are a lot of possibilities or combinations of possibilities. The battery is not yet ruled out. It may be able to power a radio, a single AAA battery can power a radio, but powering a starter, even getting it to click, is a different animal altogether.
You could start by removing the battery and taking it to a auto parts store to have it checked. If removing the battery is beyond your comfort level, then I don't think you are going to do this yourself. If you are OK with that have it checked and clean off both ends of each battery cable and the places they connect to.
If that does not turn up anything, then the next things on my book would be the safety switch (likely makes sure the clutch is depressed before allowing the starter to engage. I don't know if your 86 has that lock out however. Also the ignition switch may be bad.