Besides what Xander Bakker suggested, run topology to ensure your linework is truly connected. I mention this as much linework that represents roads, streets, pedestrian paths and such comes from CAD, which does not always snap the linework together so the lines touch. Tiny gaps, which are not readily visible, will stop a Network analysis cold. This is a very common issue.
I would suggest loading your data into a Feature Dataset in a File Geodatabase and then run Topology to ensure the linework is truly connected. Use the rule "Must Not Have Dangles". Note that this will trigger on valid situations, like dead ends, so you will have to review the results and make a determination for each case that shows up.
Another alternative is to employ this Add-in created by GeoNet Member Tim Witt, which automates the Topology process.
Topology Check Python AddIn (6/30/17)
Chris Donohue, GISP
"Network Analysis = 1% Analysis + 99% Data Cleanup"