In your comments for the question:
Although this question wasn't Actually answered, the other experts idea provided a cleaner solution. By using your idea of Pinging the PC name to get the IP address, I was able to retrieve the IP address and actually map a drive using the format \\IPAddress\ShareName
However, this created a long name for the drive under explorer instead of just a simple letter.
Reducing the PC name down to 8 characters had no effect on trying to map the drive normally.