Sounds like you have already diagnosed the problem - likely either the upper downspout is overloading the gutter below and overflowing (check next time it is raining hard, and make sure lower gutter is not debris filled), or the downspouts where then come down to the ground are dumping the water near the foundation or on ground that is too permeable or slopes toward the house. You can put an angle piece and more downspout to get the water away from the house, use a moveable gutter piece, or dig a ditch with compacted fine, packable dirt or an impervious liner to lead the water away from the house.
First, ensure the runoff from the downspouts gets at least 3 and preferably 7-10 away from the house and cannot run back toward the house - may take a bit of local regrading and compaction - but not higher than about 4 inches below top of wall AND below bottom of siding - more like 12-18 inches desireable in ground termite country.
It is also possible that when they put in the pad for the A/C they dug down rather than building a raised pad, so you have a low spot there - you may have to build a little berm around the concrete pad to stop water from running to the foundation, then a little ditch or swale (watch out for buried electrical conduit) away from the house to drain that area.
If not able to do this yourself, Gutter company or Handyman for gutter extensions, Handyman or Landscaper