As I've been playing around with OpenMediaVault, I tried running a virtual machine on the static IP address, 192.168.1.4. After getting the real machine set up and running on DHCP, I was able to log in no problem. However, changing the IP address to 192.168.1.4 (after shutting down the VM, of course) caused a problem for me. Whenever I'd point my browser at 192.168.1.4, it'd load the page then immediately reload the page, and keep on reloading.
Clearing the cookies for 192.168.1.4 resolved the problem.
I hypothesize that one or more of the cookies from the old virtual machine at 192.168.1.4 caused problems with the new, real, OMV machine at the same address.