I'm having more or less the same issue with rectangle selection. In a particular scene, I can't even select any objects with rectangle selection in object mode. And since all options are greyed out for rectangle selection in object mode I wonder which other setting might come into play.
If I start a new scene and create some cubes it still is possible to select the cubes with rectangle selection. So it seems a project specific issue/setting.
The objects I try to select have axes that are with my rectangle selection, so this should not be the issue ..