It is hard to sort out peoples problems from a distance , it sounds as if you have a collapsed sewer pipe. The surface water can easily be piped straight into the viewing inspection cover where Dynarod put their rods or alternatively straight onto the garden where it will do no harm.The sewerage side of the problem is more difficult ,is there a drain cover that gives you access to the mains sewer further down the line? If so a daily trip with a bucket may sort it short term until the old pipe is dug up and replaced.
There has not been a party ever that has been held in my house where the drains have not blocked up. Whether it is the freedom of using free toilet rolls in abundance, or other reasons I do not know. The drain rods are in the garage and it seems to be my main job as host to unblock the drains.