16 bit breadboard computer SRAM Writing Issues
In a comment, you explained that your DIP switches do not have pullups or pulldowns:


  […] when [the DIP switches] are in the up position it is connected to ground, when it's in the down position, it is floating. I can see why this could cause some problems.


Indeed, this will cause problems. Most SRAM chips will be CMOS-based, so the state of a floating input will be unpredictable.

The easiest fix will be to use resistor networks to add pullup/downs. Get a couple of SIP9 resistor packs. (Here's a listing on Mouser, but these parts are readily available from any major distributor.) These 9-pin packs consist of eight identical resistors wired like so:







simulate this circuit &ndash; Schematic created using CircuitLab

You can use these to pull all eight pins of your DIP switch up or down by attaching the common pin (on the left) to VCC or GND. Use any value in the 1kΩ to 20kΩ range. (Anything higher may not be sufficient to pull the pin reliably, and anything lower will draw too much power while pulling against a closed switch.)