Unfortunately a table saw really won't straighten lumber. No matter how good. Neither will a planer. To make square, flat furniture you need a jointer big enough to face- and edge-joint all lumber before you cut it to width or plane it to thickness.
If you don't start with flat, square stock, you won't end up with a flat square product, no matter how straight and square your joinery is.
The alternative is to flatten stock with a hand-plane. That works just as well, is only moderately more time-consuming, but requires a decent bench, truly sharp hand tools, a good long straight-edge, and maybe some simple hand-tool skills.
Sorry that you're having such a painful time with this. Let me know if I can help.
Nate