Apologies guys for taking so long to reply with how things went. I know how it's nice to get a conclusion to projects.
Where we left things last was...I was at the point of removing the clean out cap...then seeing if I could figure what the exact issue was with the backup. I tried various methods to remove the clean out cap (large pipe wrench, hitting around perimeter of clean out cap with a hammer & cold chisel, liquid wrench & tapping with hammer everywhere)...nothing was working.
This left me with two final methods to try...hitting the clean out cap hard with a big hammer to break it...or use a combination of drilling, sawing, and lite hammering). I chose the drilling/sawing/lite hammering method...since this seemed to be the least risky in terms of doing damage to parts that were not going to be replaced.
Before doing any clean out cap destruction/removal...I already had two replacement caps (plastic & brass), and plumber's putty so I could replace things right away. Basically I drilled a bunch of holes...did some cuts into the clean out cap with a jigsaw...and some lite hammering to remove the old clean out cap.
I'm glad I didn't choose the "hit it with a big hammer" to break it method. I think this old brass clean out cap was pretty old...which means it was better quality than brass clean out caps sold now. When I compared the thickness of the old brass cap to the new brass cap...the old brass cap was at least 2x as thick (maybe slightly more) as the new replacement brass cap. And I'm thinking that the old/thicker brass clean out cap probably would have need a lot more HARD hammering to break it.
But I can see how with the much more cheaply made/thin newer brass clean out caps...how the big hammer method could have worked.
Plus...after using the more "gentle" method to remove the old clean out cap...I also found out that the threads in the cast iron pipe the old brass clean out cap was threaded into were not in the best shape...and if I had used the more aggressive hard-hammering method to remove the clean out cap...those somewhat fragile old iron pipe threads may not have been useable or sealed properly after the new cap was installed.
After getting the old clean out cap removed...with a strong flashlight...I could see into the pipe & could see standing water about 3-4 feet from the clean out cap. Remember the route of the drain pipe goes straight-out from my home's foundation about 7-8 feet towards my neighbor's house...then takes a right angle towards the street for about another 80 feet. Since I had one of those small 25 foot snakes...I thought I would try this first (before renting something larger). I got to about the 20 foot mark with the small snake...and it seemed to hit something (I did this 2 times)...so I decided to go to the local Home Depot...and rent one of the 100 foot power snakes.
Remember this clean out is inside my basement where I have lots of stuff stored...so I had to hang blue tarps everywhere...since I figured that the spinning of the power snake would spray disgusting-stinky sewer pipe "jizz" everywhere...so I wanted to be prepared.
Long story short...I ran the power snake thru my homes sewer drain pipe about 4 times with different tools/tips on the end of the power snake...87 feet all the way to the street. At no time did I ever come across any roots (nothing wrapped around the tip of the snake or the snake itself)...so I'm really not sure what was partially or fully blocking the pipe causing the standing water in the pipe. But after running the power snake thru the sewer pipe 3-4 times (with different tips) 87 feet all the way to the street...the standing water cleared from the pipe...and all has been fine since.
Not a fun job...especially running a power snake inside the basement spraying sewer "juice" on the tarp covered walls...but definitely needed to be done...and I learned a lot in the process.
Thanks for all the help!