<esri:ArcGISDynamicMapServiceLayer ID="City_Intersections" DisableClientCaching="False" Url="http://gismaps.pagnet.org/ArcGIS/rest/services/ARRA_033011_2_plot/MapServer" VisibleLayers="1" />
The featurelayer link needs too look like this
Url="http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Fire/Sheep/FeatureServer/1"
Not this way
Url="http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Fire/Sheep/MapServer/1"
<esri:FeatureLayer ID="County_Intersections" DisableClientCaching="False" Url="http://gismaps.pagnet.org/ArcGIS/rest/services/ARRA_033011_2_plot/FeatureServer/4" OutFields="*" />Doesn't work yet load it as a MapService and it works fine.
The shape fields containing the geometry are hidden by your services, hence the rest end points are not returning any geometry.
You have to update your service (check the visible fields with ArcGIS desktop).
Note : ArcGIS server 10 may be more strict than previous version concerning this point.
<esri:FeatureLayer ID="County_Intersections" DisableClientCaching="False" Url="http://gismaps.pagnet.org/ArcGIS/rest/services/ARRA/FeatureServer/4" OutFields="*" />
http://gismaps.pagnet.org/ArcGIS/rest/services/ARRA/FeatureServer/4 returns Invalid URL
<esri:FeatureLayer ID="County_Intersections" DisableClientCaching="False" Url="http://gismaps.pagnet.org/ArcGIS/rest/services/ARRA_033011_2_plot/FeatureServer/4" OutFields="*" />
<esri:FeatureLayer Url="http://gismaps.pagnet.org/ArcGIS/rest/services/ARRA_033011_2_plot/MapServer/1" />