After doing research online, I found that the inlet valve often gets clogged with sediment. I removed the inlet valve from the washer and attempted to clean it on my own. This was unsuccessful so I just ordered a new inlet valve from this site. The part came really quickly and it was very affordable.
The cold water started to work once I had put on the new water inlet valve. This saved me a lot of money since I didn't have to call a repair tech or buy a new machine.