I have a basement toilet that overflows when water is drained in one of the upstairs bathroom. The water in the toilet looks completely black and doesn't go down when I attempt to us a plunger. I recently had a drain pipe break in the basement that I repaired and this started occurring almost immediately after. My house is a 2 story with a full basement and none of the other toilets or sinks are backing up or show any sign of doing so. I spoke with roto-roter and was hesitant to have them investigate because they started talking about tearing up the basement over the phone. I personally think that there is a clog somewhere in the vent and would like to get other opinions to confirm or deny what I think. Any help would be awesome and greatly appreciated.

This could be several things but it sounds like a dranage blockage and not a vent problem.. The most likely being a blockage in the drain line.
However, It could be a faulty repair job on the drain line you replaced since you informed us, " I recently had a drain pipe break in the basement that I repaired and this started occurring almost immediately after."
This makes your repair job suppect in my book. You have no choice but to snake out the drain line and find out. Good luck, Tom