MBA just had the battery repaired. Still not working. Why?

I'm exasperated.

My MBA has been in and out of the repair workshop for a month. It's two years old now. At first, the issue was that my MBA would not turn on. SMC reset wouldn't work, I tried all the tricks that were on the internet and still nothing. It is luckily still under guarantee, so I brought it back to PC world where I purchased the MBA and they took it in. It came back working fine (until I plugged in the charger which I'll touch on in a minute) with a document proclaiming that there had been issues with the top case, USB board and logic board-- these components had been faulty and had been conveniently replaced. I was shocked to hear that so much was wrong with my laptop, despite taking good care of it and it has not suffered a lot of rough and tumble at all. As I said, it was working perfectly until I plugged in the charger. When I plugged in the charger, the orange/green light was not on, and the machine was not charging. I naturally assumed that there was an issue with the charger, and I went into a local computer store to test it on two others. To my surprise, neither of the chargers worked. My laptop wasn't accepting any charge at all.

So then I sent it back to PCworld. They sent my MBA back yesterday with a document asserting that there was a fault with the battery, which had been replaced. But the same issue still persists. The laptop is not accepting any charge at all, but the machine is still turning on and working fine (it's on 20% battery and it's switched off in order to preserve whatever battery is left as I'm trying to back up my stuff). It is not a problem with the power adapter or the charger, as I've tried it on two other chargers and tons of other power adapters. I am extremely frustrated and I really just want my MBA back. I can't tell if it's just sloppy work on behalf of the repair technicians (and I hate saying that, because I really believe they try their best to do what they can) or if there's just something irreparably wrong with my macbook.

Alas, I have to send it back again, for the third time in the space of a month. You can imagine my exasperation.

Can anyone give any suggestions on what is wrong with my MBA? Why is it not accepting any charge at all? Can it be fixed -- will I need to get a new replacement altogether? Sorry for all the questions, but I really need some help.