If you check out a home theater/audio site like Parts Express, you'll find oodles of different ways to wall mount a speaker.
For heavier speakers, I've used these guys in the past with excellent results. I think they're rated for 50lbs each. Plenty of adjustability and easy installation. I used heavy-duty drywall anchors to mount mine.
Add some in-wall speaker wire and some wall plates with binding posts, and you've got a nice, clean install.
Do not use drywall anchors to hang a TV that large on a swivel mount. If it was a mount that didn't have motion, I might say that's acceptable, but not with a swivel mount.
You will need to use wood in some form to add the necessary strength.
Plywood can be attached to the wall studs using 3-1/2" lag bolts with fender washers. To provide a clean finish, the drywall can be cutout and the opening filled with the plywood. Then tape and mud the joints. Sand the surface smooth, prime, and paint. The plywood will be barely noticeable if done right. Be sure to match the plywood thickness to the drywall thickness.
If you do not want to remove any drywall, the plywood can be mounted directly over the drywall. You will need to use at least a 4" lag bolt in this case to account for the extra depth of the drywall. The plywood can be finished with a routed edge, sanded, primed, and painted for a finished look, if desired.
A final option for a truly hidden mount would be to open the wall by removing the drywall. Then install 2"x4" crossbracing between the studs at the correct locations for your TV mount. Replace the drywall, tape and mud the joints, sand, prime, and paint. The bracing is now hidden in the wall and you can attach the mount to the bracing.
Best Answer
Sounds like your sheetrock is somehow damaged from moisture or the EZ Toggle would have certainly worked. You now need to install wood backing, or move your speakers so the brackets can be screwed into the studs.
To install wood backing, first you need to cut out a rectangle of your wall's sheetrock slightly larger than the intended size of the backing panel, with the vertical cuts centered on studs. Don't try to save the old piece, replace it with new. I would use plywood instead of sawn lumber which would make a cold spot. Cut the plywood to fit flush between the studs, preferably with face grain horizontal.
Cut 2 narrow plywood strips to act as cleats. Using construction adhesive, nail/glue the strips to the studs set back from the front edge equal to the plywood thickness. Once the glue has set, nail/glue the plywood backing to the cleats. You are not supposed to nail into the edge of plywood, but in this case it's just to hold the panel in place until the glue sets.
Install a new sheetrock piece to fill the hole you cut out. Tape and mud the joints. Prime paint your finished mud job. If you have textured walls, and don't have a mud gun, there are spray cans of wall texture available for repairs just like this. Either way, you'll need to practice application to match the existing texture. Once dry, apply paint top coat to match existing wall. Whew!
Sure you can't just move the speakers to the studs? ;)