Well I know some relays are in the fuse box under the hood (found that out recently) and obviously I'd look there for a fuse also

This may seem unlikely but I'm not 100% convinced that it isn't the battery. Did they test it before you purchased it?
A while back I didn't find out a battery that I purchased had lost it's charge sitting on the shelf (presumably b/c not as many small cars w/ small batteries in my area) until after it was in the car
If I remember correctly, the car turned on and all that but wouldn't turn over. A second battery, that was checked first of course, solved the problem.