It sounds like the battery is favourite - how old is it and is the engine petrol or diesel? Diesel engines need a much healthier battery than petrol engines.
Radios etc take just a few amps, so will operate on a low battery. The starter takes hundreds of amps and might have drained the battery so low that the radio etc wouldn't work afterwards. Leaving things for a while allows the battery to recover enough for radio etc.
I've never used "a little jump-starter thing" but I don't see how these devices can supply 800 amps to turn over an engine.
Your friend's jump may have failed because of not making a good enough connection with your battery terminals - because of the large current required you can get a large voltage drop with a poor connection - this includes cheap jump leads even with a good connection.
The clutch interlock switch is nothing to do with the operation of the clutch - it is merely a switch connected to the clutch pedal which only allows the starter to operate if you have depressed the clutch. Changing the clutch will not affect it but that doesn't mean it isn't faulty in its own right although, if it has failed, it shouldn't allow the battery to drain and stop the radio working.
Faulty starter motor is a possibility.
If you can get the battery to eg Halfords and get them to test it for you. Be careful before you take it out of the car - you may need the radio code when you put it back in and there is sometimes a ritual you have to follow for the security systems on the car. On my Volvo, for example, you have to wait 5 minutes after shutting the car down before you remove the battery to avoid confusing the security systems.