iPhone 5s Needs To Be Restarted To Begin Charging

Hi all,

I am having issues charging my iPhone 5s 32GB running iOS 8.2, and the accessories involved are a lightning cable and a 3-pin power 'plug'. if it makes any difference, it is a refurbished set under warranty, and I have been using it only since mid-January 2015. The problem started recently, and not exactly at, but roughly around the time when I started to connect it to my work laptop, a Macbook Air - before this, I only connected it to my personal Macbook Pro. The problem manifests as follows:

1 - When charging with the power plug, it wouldn't charge. At first, like any normal idiot, I wiggled the power plug and it sometimes worked, but most of the time it didn't. So I connected it to the Macbook Air and it charged fine for a couple of times, then it started getting erratic as well, the problem being no. 2

2 - When connecting the cable to the Macbook Air (actually not to charge, but to transfer photos), the charging chime sounds, but after a few seconds, the charging bolt on the phone goes off. Disconnecting and reconnecting repeats the same thing.

Attempted Solutions:

- Attempted to clean the port as many people online claim is the only cause of such problems. It was completely clean as the casing I use is in such a way that the port is always half an inch away from my pocket lining, and also the phone is quite new.

- Also, sometimes a restart by holding down Power and Home buttons works.

- If the phone was first turned off, and then the cable was hooked up either to the power plug or laptop, it would power on, and most of the time it would charge fine after that, despite any wiggling and shaking to try and disconnect it.

Anyone experienced this before and found a solution? And no, I cannot take it down to the Apple Store, as I am unfortunately working on an island somewhere and won't be back to the city for another 3 weeks. Thanks for any useful suggestions!