Sounds to me like the alternator isn't charging,.youve used last of the juice in the battery to start it last time, and now the battery hasn't enough to start it now, the radio doesn't really take much power up, so that's why that is working..my suggestion is, try jump start the car, get it running, then put a multimeter on the battery to what the voltage is, should be around 11-14v if I remember rightly, any less than that, the alternator isn't charging the battery.
Alternators aren't that expensive and you should be able to fit yourself with minimum DIY skills.
Hope this helps