|This is a tough one.|
Typically, if a switch, or a port(s) on a switch fail then they stop working, period. I have an older Cisco 2900 XL 24 port sitting in my home office I grabbed from work. It has 5 bad ports that don't work. When I say "don't work" I mean, don't work at all. But all the rest do work properly so I can still get use out of it at home, but it's definitely never going to go back into production at work.
a) It's not symmetrical - i.e. X can ping Y, but Y can't ping X.
To be honest, this sounds more like a software firewall issue than anything else to me.
Try moving both to completely different ports on the switch. If the exact same behaviour continues, then it's not likely your switch but is more likely software related.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.