Can't no longer sync iTunes with iPhone 4

I have an iPhone 4 and I'm using the latest iOS for it, 7.1.2.

The Mac I am using to sync music manually with the phone has iTunes 12.3.0.44.

At first, I had music on the iPhone that I was not able to delete. When the phone was synched with my Mac, I would delete the songs on my device in iTunes and sync the device, but when I restarted my phone, the songs were still there.

I then deleted all the songs from my phone via iTunes and and synched the phone. Now, all the songs from the device are gone (except for 2 songs), but when I connect my phone to my Mac, I see a bunch of other songs with the dotted grey circle in iTunes and I can't sync any new songs to the device.

Any advice is greatly appreciated!

iPhone 4, iOS 7.1.2