I don't think there's any reason to be without hope. I've gotten into grad school with 0 work experience (straight out of undergrad). I would say you should certainly have hope as long as your grades were good in undergrad and, yes, you use your statements in part to explain how you've spent the last 4 years (and how they have motivated you to graduate study). Hopefully you can find some recommenders from your undergrad days, or from other work experience-- it sounds like you have some work experience in the last few years, just that you don't think it's super related to what you want to do. There are so many grad programs out there, and you seem very well spoken, so if you can rustle up those recommendations AND articulate why you want further study in your field, you should be very hopeful!
That said, there are tons of non-receptionist jobs out there for people with non-technical degrees, so don't immediately write off the possibility of gaining more work experience!