You are most likely correct in the ground thinking. Sometimes ground problems are hard to get quiet due to the nature of single coil pickups yet they do sound they best with many sweet tones that humbuckers can not do. Be sure you have a very good quality guitar cord with proper shielding and the jacks are well grounded from the guitar output all the way to the grounding of the amp.

It is not likely you will get rid of all the noise though unless you use a ground filter unit something like a Hush brand noise filtering unit. I use the Hush II unit and it works very well.

Sometimes the problem is due to things like fluorescent lighting nearby or even poorly grounded electrical outlets wherever ypu may be pluged in for power. The best thing is to get the filtering unit and trim it out. Single coil pickups actually work on the basis of EMI which is electronic magnetic interference or electrical magnetic interference. This is where the electro magnetic field picks up trash interference from radio signals to small ballasts and transformers that produce high frequency hums into the field of the pickups. Unfortunately, that interference is what makes the strings interfere in the field which makes them sound so good. You kill that problem completely and you destroy the sweetest tones you ever heard from the single coil pickups.

I found the best of both worlds is to filter out the trash and keep the sounds. Hope this is helpful.