Lets see,
Dzl, excellent technical soil analysis explanation. Kudos.
Depending on when your house was built, you have both outside and inside drain piping. Along the footing outside your house you have drain piping that is piped INTO your house through bleeder pipes in the footing and this is piped to your sump crock.
If the house is old, you have VCP vitreous clay piping that could have collapsed both inside and out. If the house is newer, the bleeders may have gotten plugged up outside or inside with mud/debris etc.
If you are interested in a permanent fix, you have to dig up and install new bleeder lines inside and outside.
People charge BIG money to do this.
You CAN do this yourself, depending on how handy dandy you are. Go to a house site that is having the basement installed and study what it looks like. ONLY DIG UP ONE SIDE OF THE HOUSE AT A TIME!!!! No more than 40-50 feet or so, or you can have collapsed walls. You can have a company come out and spray coat the side of the dug up basement with Watchdog plasticized basement waterproofing spray to fill in cracks and seal the wall.
Make no mistake, this is rather expensive. Unless you rent the mini excavator and do it yourself.
Best of luck!
Dram