Is there a way I can use the delay command and have something else running in the background?
Kinda, if you use interrupts. delay itself uses these. But it's not as elegant as a multi-threaded solution (which is probably what you're looking for). There is a Multi-Threading library for Arduino but I'm not sure how well, or even if, it works.
The Arduino is only capable of running a single thread at a time meaning it can only do one thing at a time. You can use interrupts to literally interrupt the normal flow of your code but it's still technically not executing at the same time. The library I linked to attempts to implement what you might call a crude "hyper-threaded" solution. Two threads executing in tandem on a single physical processing core.