My Linux computer (hostname "apst") is in the same workgroup
as my Microsoft PC running Windows 2003.

On my Linux host, I have the following section in the smb.conf file:
[public]
path = /home/public
public = yes
only guest = yes
writable = yes
printable = no

When I typed the command
smbclient '\\apst\public'
the following message was displayed:
added interface ip=192.168.1.8 bcast=192.168.1.15 nmask=255.255.255.240
password:

I typed in the password for the owner of directory /home/public.
The following text was displayed:
Domain=[WORKGROUP] Os=[Unix] Server=[Samba 2.2.7a]
Smb:\>

This shows that I can connect to a file service.

I then go to the DOS command screen on my Microsoft PC and
typed the following command to map network drive g:
net use g: \\apst\public

The following error message was displayed:
System error 53 has occurred
The network path was not found

I then tried the following:

From the Microsoft PC
My Network Places --> Computers Near Me

I can see "apst" under the "Name" column with
comment "Samba server"

But when I clicked on entry "apst", the following error message
was displayed:

"Network path \\apst is not accessible"

Do you know what could be causing this problem?

Thanks!

i say why don't you just do a reverse??
what i mean was that let window share the partition.
Then linux must see it. then just do whatever your want

Seems to be a NetBios name resolution or computers are not in the same subnet.

Ping from Dos by ip Linux box.
Ping then by name in both direction.
If this okay then NetBIOS name resolution is out of problem.

Then check if your Microsoft PC got an address between (excluding ip assigned for linux box):

ip=192.168.1.8 and ip=192.168.1.14
and subnet mask is 255.255.255.240.