Connectivity Problems After Battery Install

My battery in my A1370 Mid-2011 Mac Book Air swelled so I took it out. It still worked it just had to be plugged in. I installed a new iFixIt battery and it worked without the plug.

I couldn't, however, connect to my wifi network at first.

I reset the NVRAM and the SMC. Eventually, I was able to connect, however even though it said I was connected to the network I couldn't get online. The WiFi bar was full but when I connected it said I had no internet service.

At one point I got connected and got online and had it working fine. But it keeps going back and forth between not connecting at all and connecting but not getting on the internet. Please help! Please and thank you!