The dash lights you mention and radio means nothing, they need minimal power, the starter needs massive power and so a healthy battery to do so!

Battery would have to be bad if it wont even turn over, usually you get a lot of rapid clicks though from the solenoid in this case, check the connections as said first and also make sure they are not corroded!

Anyway easiest thing is to turn the headlights on and inspect if they are bright, if so then the battery is good, if they are an orange glow or dull then it's bad.

If you bump start it won't tell you much either as again this only needs mininal power for ignition system etc, so you won't know if it's starter or battery.

Martin