These two steps should help in these scenarios:
1. Put entry of the old machine name in 'Client's HOST file'
2. Then open map documents to check for the broken links.
1. Add following entry in the client's host file in system32\drivers\etc folder:
'127.0.0.1 old_Arcsde_server_name' |
This will point the name-to-IP resolution back to your machine causing the connection attempt to fail immediately instead of timing out for each layer.
2. Then resource the MXD again:
a) Access the map document from ArcCatalog - Right click - Set datasource(s)... - Select All -Replace All
b) Right click on the new connection - Properties - Copy the path that you see in front of Name
c) Put the above path in front of Replace with:
Replace with: new connection file path