tell the dealership to jump start the car (as you have been doing) and check the charging system. They can check the alternator output, battery's ability to take a charge/load etc. Sears does this for free, BTW.
There is an old saying: "Mistrust breeds contempt" ….. You used "Stealer". I would suggest you try Sears or another establishment that you can have confidence in and that you can trust.
If you decide that the dealership is where you are going to have your car serviced, approach the situation from the other side: "Go ahead and install a new battery, but be sure to substantiate (prove) that I need one". That is a very reasonable request and is easy to verify. Our '95 wagon got a new one two years ago. I think the previous owner ran it out of H2O, but that's a guess.
The battery is a constant and a needed/dependent element in your cars electrical system. A battery with 10 volts is not good and that is why you got all the relay clacking AND why it wouldn't start, except with a jump.
Obviously your battery is good to supply some of the load balance on your electrical system, but does not retain enough juice to start it. It could be an alternator problem resulting in not charging the battery.
My 2 cents
'03 E320 Wagon-Sold
'95 E320 Wagon-Went to Ex
'93 190E 2.6-Wrecked
'91 300E-Went to Ex
'65 911 Coupe (#302580)