Questions:
If all the machine have a static address, what is DHCP handing addresses to? Be sure that the computer named access does not have a lease
When you set machines to static are they given IP addresses or reserved in DHCP?
Steps to try
In DNS check that the (A) record name correlates to the IP and check that the PTR record IP match the host name
From a machine that can map the drive perform an NSLOOKUP on the IP and hostname then perform the same action on the one that does not work. If you have more than one DNS server look at the DNS server that is being used in the NSLOOKUP command. Check your network adapter settings where DNS Server is configured to make sure it is the same between both machines.
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