A computer's SID is stored in the Registry's SECURITY hive under SECURITY\SAM\Domains\Account. This key has a value named F and a value named V. The V value is a binary value that has the computer SID embedded within it at the end of its data.
As far as i can tell, you have to grant rights to the admins to access this registry key. If not, the only the "system" account has access to it.
example:
"V"=hex:00,00,00,00,e0,00,00,00,02,00,01,00,e0,00,00,00,18,00,00,00,00,00,00,\
00,f8,00,00,00,00,00,00,00,00,00,00,00,f8,00,00,00,00,00,00,00,00,00,00,00,\
01,00,14,80,c0,00,00,00,d0,00,00,00,14,00,00,00,44,00,00,00,02,00,30,00,02,\
00,00,00,02,c0,14,00,7a,04,05,01,01,01,00,00,00,00,00,01,00,00,00,00,02,c0,\
14,00,ff,ff,1f,00,01,01,00,00,00,00,00,05,07,00,00,00,02,00,7c,00,05,00,00,\
00,00,00,14,00,85,03,02,00,01,01,00,00,00,00,00,01,00,00,00,00,00,00,18,00,\
85,03,02,00,01,02,00,00,00,00,00,05,20,00,00,00,21,02,00,00,00,00,18,00,df,\
07,0f,00,01,02,00,00,00,00,00,05,20,00,00,00,20,02,00,00,00,00,18,00,d5,03,\
02,00,01,02,00,00,00,00,00,05,20,00,00,00,23,02,00,00,00,00,18,00,d5,03,02,\
00,01,02,00,00,00,00,00,05,20,00,00,00,24,02,00,00,01,02,00,00,00,00,00,05,\
20,00,00,00,20,02,00,00,01,02,00,00,00,00,00,05,20,00,00,00,20,02,00,00,01,\
04,00,00,00,00,00,05,15,00,00,00,21,58,8a,12,2c,2b,74,58,27,30,c9,dc
the SID I'm searching in this now is:
S-1-5-21-311056417-1484008236-3704172583