Hi,
I'm assuming that you have enabled named pipes for both SQL instances.
1-Network Issue
Looks like you have problems with domain name resolving.
C:\Users\administrator>ping -a labsql
Pinging labsql.LAB.com [208.87.35.103] with 32 bytes of data:
Reply from 208.87.35.103: bytes=32 time=329ms TTL=128
Reply from 208.87.35.103: bytes=32 time=313ms TTL=128
Reply from 208.87.35.103: bytes=32 time=303ms TTL=128
Reply from 208.87.35.103: bytes=32 time=311ms TTL=128
C:\Users\administrator>ping -a 10.0.0.15
Pinging LABSQL [10.0.0.15] with 32 bytes of data:
Reply from 10.0.0.15: bytes=32 time<1ms TTL=128
Reply from 10.0.0.15: bytes=32 time=1ms TTL=128
Reply from 10.0.0.15: bytes=32 time<1ms TTL=128
Reply from 10.0.0.15: bytes=32 time<1ms TTL=128
C:\Users\administrator>nslookup 10.0.0.15
Server: UnKnown
Address: 10.0.0.2
*** UnKnown can't find 10.0.0.15: Non-existent domain
3-Firewall Issue
Make sure that you don't have any filters/switches/firewalls somewhere between NS and SQL machines; otherwise they should be configured to allow SQL connection.
4-Client Driver Issue
C:\Users\administrator>telnet labsql 1433
Connecting To labsql...Could not open connection to the host, on port 1433: Connect failed
Let's assume that you have telnet installed and enabled on both machines. Looks like "labsql" name is mapped to incorrect IP address, or port/telnet connection is blocked somewehere between "LABALTIRIS" and "LABSQL".
Also, don't specify "MSSQLSERVER" if you have default instance, because it will look for non-default instance named "MSSQLSERVER".
You may try same steps, but with IP address of SQL server and "sa" user.