Basement water intrusion in WNY (unfinished basement) - moisture tracking down interior wall cracks. Advice?

Hi all — I live in Western New York. Split level home with an unfinished basement with water seeping in after heavy rain and snow thawing. I took some photos and it looks like the water is tracking down a couple of vertical hairline cracks on the wall near the floor. I’ve also added several pictures for visual references.

For some additional context, it’s the basement wall that is a part of the concrete slab that the lower level of the split level sits on. This wall is also where the copper piping for our radiator heating system runs into, as seen in Photo #1.

What I’m seeing:

• ⁠Vertical staining down the wall from a few small cracks. • ⁠Active moisture on the surface after rain/snow melting (not just old staining). • ⁠The leak is slow seepage, not a flood, but it’s consistent. • ⁠No previous repairs from the look of it? Not 100% sure of this, though. Basement walls seem to have been painted, I’m just not sure if that would be considered a “repair” in the waterproofing sense. • ⁠No exterior waterproofing, no sump system upgrades, no visible crack injection — looks untouched.

I have little-to-no experience with DIY stuff, but I am willing to do most DIY things unless a professional job really is the play here compared to any DIY options.

Any guidance or next-step priorities would be really appreciated. Thank you in advance!