Can you ping it by IP AND by name from the Lansweeper machine ?
If yes, the we can rule out DNS/Netbios issues...
Is there some kind of firewall/ACL's between the VLANs ?
Something that blocks the DCOM/WMI Ports ?
Also, and that of course depends on your setup, changing the
LAN of a machine can make Windows change the Network Location
for the machine (from home/work to public, for instance) and
that triggers the local firewall... that should have blocked
the ping, but stranger things have happened...