Battery Replacement Charging Intermittently

I just finished the battery replacement kit for the MacBook Air 11" 2010. Worked perfectly, and the battery is able to power the computer without a power supply. But when I plug the Air into the power supply, the battery reads "Not Charging." After a few minutes, this issue clears and reads as charging, but then after a minute more, it goes back to not charging. I discharged the battery to 30%, charged ok after that until it got to around 73% and the issue presented itself again. Power supply indicator light is just as patchy. Battery reads as normal, but the charging is very patchy. Any ideas? I already reset the SMC (several times) but to no avail. Also the battery reads "1 Complete Cycle" which makes sense as it's a brand new battery. And according to coconut battery, when its charging, the charging wattage reads .4 watts, nothing compared to the so-called 45 watt power supply meant for the Air (and I tried two different power supplies already). If there is a setting that makes the Air stop charging at full speed to reach what it thinks is the full capacity, can I turn it off? (I noticed that the replacement battery had more charge than stock.) Please help! I really want to keep this Mac alive.