My Apple iPhone 5c will not sync with iTunes

Hi everyone, I'm here to ask if anyone has encountered the same problem as me and fixed it or simply has an answer. I've fiddled with my phone for several hours now, all because I wanted to transfer some new music to my iPhone. When I was originally trying to transfer my music over, it wasn't highlighting my phone indicating that the music would transfer over, I go over to the phone in iTunes, which is identifying it exists but not syncing, I clicked everything necessary to transfer it such as: Manually manage music and videos, Sync this phone over Wi-Fi, and under the music tab I selected Sync Music. Yes, this is on a different computer, a new one but even then, it's not picking up or syncing with this computer and the phone itself is no longer attached to my old one because I reset it. I've said yes to erasing all the music and sycning with this library but it still doesn't work. It's as if the phone doesn't recognize the computer and it just charges but iTunes on the computer recognizes the phone because I've headed to settings and used "iTunes Wi-FI Sync" under General and it tells me to plug my iPhone in via USB when it already is, and I have tried plugging it in and out. Because of this, I don't think I can make a new iCloud backup of my current state in my phone, any answers? I might add in more later to this.