Rapid clicking and dash lights dim - Flat battery or low battery voltage to starter motor
Take extreme care jump starting Di models - the ECU is prone to voltage spikes
Check battery terminals are tight
Check battery earth straps to front panel and to chassis and gearbox are secure and in good condition - the earth strap to the gearbox can burn out and corrosion/breaking of the connector on the front panel is common
Check battery positive connection to starter motor is secure.
If the battery has gone flat investigate the cause!
If a known good battery goes flat with no obvious cause check to see if the alternator is warm even though the engine is cold. If this is the case then a new alternator may be required (a faulty diode in it is allowing the battery to discharge through the alternator windings).

No noise - Dash lights do not dim - no feed to starter motor
Check/clean/adjust small plastic spade connector on top of the starter motor - its a common failure
Check battery, power and earth connections as above.

Beeping from the car - Immobiliser activated
Use the keyfob to deactivate the immobiliser
If this fails try the other fob
If this also fails try using the key in the lock
If this fails try disconnecting the battery and reconnecting it (making sure that you have the keys with you). Then press the unlock button repeatedly until the car unlocks.