I have a couple of A-mount Sigmas (70-200 f2.8 and 100-300 f4) that works pretty okay on LA-EA4, even with an 1.4x extender. But I do know that some of the older Sigma A-mount lenses need to be sent to Sigma for a FW update in order to make them work properly on a SLT body (which the LA-EA4 pretty much is).
This would be my first suspicion, unless it was for the fact that they work on your A77...
What focus mode are you using in your A7? AF/MF/DMF? Remember, the setting in the camera can override the setting on the lens. If I slide the focus ring on my Sigma 100-300 f4 to manual, AF will still kick in, unless it's set to MF in camera.