If you are not using an iPhone in the standard position, you have to remove the (Lightning ended) cable at the top-left corner of the controller from the controller. Weird but true.
Your kit should have come with replacement cables (micro-USB and USB-C) if you want to use another sort of phone there, or you can use the USB connector at the front of the controller with any cable but you must disconnect the (Edited = what was I doing?) standard cable before that will work.
As Idrach mentioned, the controller will not connect to a device when using the bottom/larger usb port if there's a cable attached to the upper left. A number of folks prefer using the bottom/larger one as it seems more reliable.
By the way, you can attach a power bank to the upper/left port for charging and still use the lower one. But even leaving an unattached cable plugged in to the side port disables the lower port.
I'm sure you already checked but did you try using canned air to clean the ports? It's easy to get something in there that will fail the connection. Also, did you upgrade firmware and all that? You could be connected and if there is a update available you'll need to let that run before the connection can be made.