If alarm sounding and remote control key fob not working, open car with key alarm will sound, start car alarm will stop and go into standby, you can then use car until fixed, it will go of every time you open car.
Keyless entry, if parked with wheels turned or against kerb etc. You may have to rock steering wheel or turn against load on tyres as engine is started to allow steering lock to disengage.
Toyota Prius Hybrid can suffer a flat auxiliary battery (12 volts) this can be jumped started in the recommend way. It is normally in the boot and early cars can be easily accessed here, later cars have a jump start point under bonnet (under red cover on bulkhead) or in the fuse box see picture. You will need to keep your foot on accelerator pedal for 15 minutes to charge battery or engine will stop. Don't touch any of the high voltage wiring (orange connectors as these are for the 288 volt motor and will kill you).
Use the advice links above to help diagnose your non-start, immobilizer, warning lights, and engine or general problems.