I selected my light and did the necessary mouse move to enable me to rotate an object. I got a white dashed line for the view line of the light which swung 360 degrees. But when I click it goes away and the light source stays in the same position.
You can rotate things by hitting r key. You can lock the rotating to axis by hitting the alphabet of axis after hitting r. For example hitting r and then x twice allows you to rotate an object in its local x axis. Note: global and local axis are different things. Make a cube and rotate it and you will see what I mean.
It may be that your lamp is ordinary lamp that cannot be rotated. It radiates everywhere. There are other lamp types that can be rotated.
Also don’t forget that if there is an IPO that’s affecting the position of the light … as there might be, from your previous attempts to animate the light … then that IPO will prevail unless you modify it by means of a keyframe.
Select the lamp and switch to an IPO-window. If there are RotX (etc…) IPO-curves present, then you should see a vertex on those curves anywhere you’ve declared a keyframe. The rotation established by that IPO is going to prevail until you either remove the IPO or change it.