If it is only a charging problem you may be able to find someone with a charged battery to confirm. There are Fairphone angels around and about who may be able to suggest some thing or someone close to you.
You may also be able to get the battery charged independent of the phone, again to ensure it is a charging problem.
There is always a possibility that the bottom module may ruin a charged battery if it has a fault so it may be possible to see if the phone switches on with a charged battery with the bottom module removed. Again a Fairphone angel with FP2 experience would be able to let you know.
If you look at the image below and compare you may be able to tell if it is a fatigued soldering connection, which could be fixed.