Maybe the battery is knackered as a result of running down for a couple of cold months and wont take a charge.
Before buying a replacement battery, i would give it an overnight trickle charge and see how it goes.
If its a 2013 model, the battery is possibly reaching the end of its life anyway, particularly if the car has not been used regularly.
I often suggest that before replacing a battery, people have their alternator output checked and have the voltage of the old battery checked.
Ive seen too many people conned inro replacing perfectly good batteries when they just need a charge or have another fault like an alternator issue or simply a stuck switch leaving a boot or interior light switched on (in fact this is the first thing i always check).