I have a street shp file that I am using the ArcCatalog procedure to create a network dataset. I am not including elevation and have then set up the service area in Network Analyst and I usually get no answer at all when I use 3 minutes for the calculation. If you need additional information, please let me know.
It was hard to see where the location you were trying to do a service area around from your image. Can you focus into that location and its surrounding streets? Alternately, chose a new location and see if a service area can be applied around it. Of course this assumes you have a time field in your table (ie minutes) to use as the impedance rather than the default segment lengths.
Okay, so I double checked my timecost field and it is there and filled in. I created a new network dataset and added it to my map. So this is the map I got when I tried to have service area from the two stations 35 and 36.