Drain tile issues and wet basement

I am having an issue with water coming up into the basement of my home, and need some info and advise.

First, some history on the house itself. The original house was built around 1899-1900 per the county records, and we have met the grand-daughter of the guy who built it, she was born in it..
The original house stood on a field stone foundation over a crawl space and had a small root cellar under a small part of it, also hand laid field stone.
At some point, the basement was dug out and the basement walls were built of concrete block, about 1/4 of the house was left on the stone foundation walls. An 8 foot round, 20 foot deep cistern is alongside part of the cinder-block foundation wall on one side of the house.
In the late 70's, an addition was built on, and the basement expanded, and the addition was built on a poured concrete foundation.

A floor drain was installed in the "new" part of the basement, connected to the drain tile on the exterior side of the foundation wall.
I am of the opinion that there is probably no drainage around the old stone foundation or cinder block areas, but that a drain tile was installed along the poured areas of the foundation.

We have been here 4 years and never had any major issues until a couple weeks ago when we had 4 days of rain/snow after 2 major snow storms a week apart each.
I went down and found water coming up through the floor drain... not seeping, but bubbling up like a fountain, 2-3 inches high!
I plugged the drain and we pumped out the basement, to find water continued to seep in between the slab and the foundation walls..this continued for about a week before finally drying out yesterday.
We have had 2 years of severe drought and dry weather, and although we watered the foundation walls weekly, I figured the drain tile had settled and broken.
I had a plumber come out and snake the drain tile through a window well drain, he found it was clear for about 35 foot, but then was blocked. He scoped it and located the blockage for me and left..
The blockage was were the poured foundation met the old stone foundation, at the old cellar door entrance.
I hand-dug down to the tile and discovered that there was no break in the pipe, the pipe simply ends there... no plug, no drain, it just stops... and the back-fill is thick grey clay, that allows almost NO water to pass through it.

I currently have the end of the pipe exposed, and if I run a garden hose down the window well drain, water slowly comes out the pipe..but it seems to me that it flows out slower than I would have expected..
My question is, how fast should this be flowing, and is it normal for the pipe to just stop with out being day-lighted or going to a sump?
I am trying to decide if I need to simply connect to the end of it and day-light it, or have the whole thing replaced. there is a day-light drain a few inches lower than the drain tile that I could easily tie into , just means a few more days digging..
The pipe is 6 inch clay pipe, with no gravel bed or anything around it, and only runs for a total of 80 feet, around two walls of the foundation.
The estimate to replace it is not too bad, but I dont want to destroy my wifes flower beds if I dont have to..
Heres pics of what I am talking about :
Attachment 12494
The open end of the drain tile, laying on top of the footing, the back fill is all clay
This pic wont display for some reason, it is down nder " attached images"

the ground slopes away from the side were water was coming in, the window well drain is under that red can you can see

This is the door way that once was the cellar entrance, the cinderblock replaced the field stone, and its poured concrete on the other side of it.

The floor drain that attaches to the drain tile, and you can see where the water was seeping up between the slab and the walls

the old stone foundation meets the poured concrete..

 

I see no reason you couldn't tie this drain into the other one. I would remove all of the blockage. You want the water to be able to flow freely inside the drain.