Well, let's clarify a couple of things.
a. No AV program existing...blocks access to shared folders/files, etc.
b. A firewall might do that, but no legitimate AV program has that power. Firewalls block access, AV programs don't even block access to malware unless programmed to do such by the owner, that's why program configuration is important.
c. Malware might also block access to files on the system.
Now...if you think that installation of a malware-defense program...causes changes in your ability to normally access files on the system...I would have to guess that you have mispointed the culprit.
Have you taken a look in Event Viewer for possible clues?
How To Use Event Viewer - http://www.bleepingcomputer.com/forums/t/40108/how-to-use-event-viewer/
Secondly...if you have problems accessing files from 1 computer on a network...but no problem accessing other systems on the network...maybe the problem is with that system, not with yours. That is, assuming that no other systems experience what you experience.