Rog,
IF you were to drill some holes in block and some water came out,this MEANS there IS........Water Inside yer blocks. lol

It has absolutely NOTHING to do with what 'opinion'said. It simply means, water is getting INTO the Inside of hollow Blocks because of an Opening(s) on the Outside of the wall and/or, an opening(s)ABOVE ground level.
Could be openings in/around bricks `n mortar joints,siding,around front door & threshold,we have seem small openings around 'door bell' actually be WHY `n where water entered. Sometimes ya have to look REAL close to see/notice smaller kinds of openings which can allow water inside.
Has ZERO to do with 'existing drainage system'...No way man.
Excessive indoor Humidity OR what i have described is most likely your probelm(s).
If you ONLY get water/dampness when it rains, then its probably not indoor humidity.
You could recreate a heavy Rain with a hose to see where problems are.
get a hose and run it next to/near house at ground level on, the outside of where you see damp spots inside. let it run for up to 1 hour. if you do NOT see water/dampness in an hour, wait and check walls again later in day.
If still NO water/dampness then next dry day ya get, HOLD the hose and run at just above ground level against lower bricks/siding whatever. go side to side slowly, soaking the crap outta each small area as you work your up.
Have someone Inside basement watching for FIRST signs of water/dampness! When they see ANY changes then what you were just soaking/wetting is part/all of the problem.
again, while soaking home above-ground, pay close attention to Any small openings. you have to soak each area good as ya work side to side and UP. Other potential openings could be mortar joints,cheap-porous bricks,around any door, around any window, light fixtures,where central a/c hose enters house etc. Even openings in a valley of a roof have been why a few have gotten water/dampness inside.
M Blues....each day has it`s always
a look down life`s hallways,
doorways, to lead you there