The most obvious cause is that both instances are sharing a resource that should not be shared. The advice about using File Monitor and Process Monitor to help detect this is worth looking at.

You say you are using SQL 2008 (not SQL 2008 R2). This version uses 8.3 style filename references for some of its folders, and I remember a situation a few years back where the installer plugged in the wrong 8.3 reference for a folder. This resulted in two instances using the same folder when looking at 8.3 format filenames, while the long format filenames were correct and distinct. Needless to say only one instance at a time would work. I could not reproduce the problem so did not report it.