CHarge port replaced-computer dont recognize
Most rooting techniques require you to connect the phone to a PC via USB in order to unlock the bootloader, so you won't be able to root the phone this way without a working USB port. Some phones have security vulnerabilities which allow you to root the phone from an app (such as Framaroot), but this only applies to specific phones and specific firmware versions which have such a bug.

It's certainly possible for a port to only charge and not transfer data. In a USB port, there are two data pins, a +5V power pin, and ground. If either of the two data pins are broken or not connected properly, you can still transfer power over the power connection, but no data can be transferred. Most likely these pins weren't soldered correctly when your new USB port was added.