[morzh]

The reason probably was the capacitor either leaking grossly or shorting.
It is desirable to replace it as it is a decoupling cap, but it will work without it.

Now as to should you replace the other two....I would, as again, they are decoupling caps and are exposed to the raw power voltage, so if they go, they will possibly take something in the power supply (choke, field coil) with them.
Or you could try your luck.

Were they RC filter caps I'd say "if the radio works well, leave them", but in case of decouplers I am pro-active.