Noticed that the example didn't quite come out right. Darn those spell checkers. So let me go over it and clarify a little.
If you can ping by both name and IP then you don't need to add anything to the HOSTS file. Likley the LMHOSTS as well.
Before doing that, to test to make sure it is not just a browsing issue, try manually making a network connection using the computer and share name (this is where the typo came in)
From a command prompt:
net use x: \\computer_name\share_name
From the Windows Explorer
Tools / Map Network Drive
Select a drive letter
For the path enter \\computer_name\share_name
If either one still can't resolve the computer name, then edit the LMHOSTS file. With W2K it is in the \windows (or \winnt)\system32\drivers\etc directory. For Win9x it is in the \windows directory.
The syntax for either one is IP_Address followed by the computer_name (the number of spaces between the two is not relevant.
e.g. 192.168.0.2 computer1