Can a table have two primary keys
Absolutely no, period. The fact that separate unique constraints can be defined does not make them primary keys as well.
Similarly, a table could have 999 unique constraints that didn't allow nulls but not have a primary key.
SQL DBA,SQL Server MVP(07, 08, 09) Prosecutor James Blackburn, in closing argument in the Fatal Vision murders trial:
If in the future, you should cry a tear, cry one for them [the murder victims]. If in the future, you should say a prayer, say one for them. And if in the future, you should light a candle, light one for them.