YOU CANT SEAL WATER OUT! YOUR BASEMENT ISNT A REVERSE BATHTUB!

The ONLY solution is redirecting the water from away and under your
home. the high basement humidities just lead to mold growth even if
the water isnt puddling inside.

the cheapest solution is a indoor french drain with sump pump to move
the water far away from your home

I agree with bob haller on this.

What causes basements to leak is an over saturated soil around the
foundation. A hole was dug, in order for the basement to be built.
After the walls were up, the area around the foundation was back
filled with dirt. That dirt is more lose and more porous than the
undisturbed soil around it and it takes many years, sometimes decades
for that soil to settle and become as hard packed as the undisturbed
surroundings.
Therefore it acts like a sponge, soaking up rain water, and in your
case the sprinkler water as well. The resulting hydrostatic pressure
causes the water to infiltrate the basement walls, through cracks in
the concrete, through the joint between the floor an the walls, and
through the porous concrete itself due to capillary action.
Therefore the way to keep basements dry is to keep that soil around
the foundation as dry as possible.

Slope the terrain away from the house, keep gutters clean and
downspouts discharging as far as possible, keep sprinklers and hoses
away from the walls as well as any plants that need constant watering.

However you can't prevent rain from soaking your yard. And this is why
houses are built with a french drain buried by the foundation footing.
To help relieve the hydrostatic pressure by draining rain water and
discharging it somewhere. Unless your home is very old, chances are
that you do have one in place, hopefully in charge of diverting the
water to that sump pump you mention you have. (I say hopefully because
we've seem houses in which the drain tile is tied to nothing and leads
nowhere, believe it or not.)

The problem with those drain tiles is that, they fail overtime. Which
is what probably happened in your case, after 4 years functioning
properly. It is probably clogged or collapsed. In addition, because
they are buried, they can't be serviced when collapsed or flushed
when clogged with mud and debris without digging out the foundation
(and then making the dirt around it all loose and sponge-like again
when you fill it back) and replacing the drain tile. If you have
porches, decks, fixtures... well they will have to come off too.

This is why internal perimeter drainage systems were invented, and
have been used successfully for over 20 years. They work like the
external ones do: collect the water from the surrounding soil, divert
it to a sump pump which gets it out and away from the basement. They
can be installed internally, with much less disruption, for a fraction
of the cost (about 50% less) of digging out foundations, and can be
fully serviced over the years, which is why good reputable companies
offer lifetime transferable warranty on them.

Just make sure you pick a company that has been in business long
enough, so that you know that they will be there for years to come to
to honor the warranty they give you, and good companies usually don't
have obnoxious sales tactics. Call 3 in you area and sign nothing you
are not absolutely comfortable with.

Oh, and one more tip. Even if you do sign something and then regret,
every state in the US has a version of the FTC cooling off rules,
which gives you a certain amount of time (usually 3 days, some states
less, so please check the time in your area) to cancel any contract
signed or purchase made outside the provider/seller's place of
business, (that means your home), without incurring in any
cancellation fees or penalties. This rule was created exactly to
protect people from pushy door-to-door sales people. So feel free to
shop around until you find a company and system that really makes
sense to you.

Hope this helps.