Replacing sewage pipes

[Brahnla]

My home is 85 years old and has all the original plumbing. The toilet keeps backing up and raw sewage flows into the bathtub next to it. I had a new sewage line and trap installed outside the house (next to where the toilet is) to the city sewer access in front of the house. The lines have been snaked repeatedly and the toilet keeps backing up. I'm pretty sure I need to replace all the sewage/discharge pipes under the house. Any tips?

 

[Brahnla]

More about my plumbing problems

I just washed the dishes and sewage poured into the bathtub. The laundry sink is also clogged. I've never replaced pipes before, but I've done a lot of different types of construction (drywalling, refinishing hardwood floors, building cement block walls). Should I do this job myself or hire someone?