Why does this new HVAC have open holes in the side?
[ Edited to reflect that this may or may not be outside vented and may or may not be dangerous. If you upvoted mainly because I warned of the dangers, now's your chance to remove it :) ]
That is a high efficiency heating system.  It uses a PVC pipe instead of a chimney for its exhaust.  There are two kinds. Some are &quot;direct vent&quot; that use another PVC pipe to ingest air from outside for combustion.    The other kind uses air from the room around the boiler for combustion (but still exhausts to the outside).
Hopefully yours is is designed to consume room air, as more thoroughly described in another answer, in which case the empty hole is where it gets its air.  If it's properly installed it will be in a room large enough to provide it plenty of air for combustion, or in a smaller room with one or more vents into larger spaces.  You should check the model and the manual to see if it is installed correctly and in a large enough space.
If yours is meant to be direct vented (consume outside air) it would have a second PVC pipe going outside.  Your manual will tell you.   Hopefully that's not the case but if it is, you should not use this for heating until it has been fixed.
Either way it's a good idea to install a CO detector near the unit.   As little at $15.  Some give you a reading so you know if it's non-zero even if not at danger levels.
All of this relates to heating.  I don't have an answer to the issue of not cooling.