Black screen (no boot up) after upgrading RAM to 16GB on mid 2010 macbook pro
According to everymac.com your MacBook Pro probably neither supports 16 GB nor PC3-12800 memory modules. There is one exception for the MacBookPro7,1 (MacBook Pro Mid 2010 13") which supports 16 GB.

If you happen to have a MacBookPro7,1 get two 8 GB PC3-8500 modules or in all other cases get two 4 GB PC3-8500 modules.