Reading/Writing An SRAM Chip with an Arduino
I think maybe you are not disabling the data bits of the 74xx95 outputs, so they are fighting with the RAM data outputs.  Logic '0' outputs tend to win when a '0' and '1' are both being driven onto a signal line simultaneously. You need a method in your circuit to float/disable/tri-state your 74xx95 outputs so the RAM outputs can take over. 

From the level of detail I can see in the trace it's looks pretty clean.  But there isn't enough resolution to see what the CE and WE are doing precisely.