I have some simple suggestions on how you can repair your two toilets without calling a plumber. For the first one, which doesn't flush everything away consider trying these few steps: First, check the level of water in the tank. If the tank isn't filling full enough, it can't flush with enough pressure. If there is no obvious water level line, the correct level should be within one inch of the top of the overflow tube. Second, scratch away the mineral deposits that have been building up in there for the last ten years. To do this, take a small nail and poke it around in those little holes under the bowl rim. If the toilet has a little hole near the bottom of the bowl, scratch around in that, also. You may get quite a bit of gritty residue out, and this will allow the toilet to flush with much better pressure. Third, snake through the toilet with a hand tool known as a closet auger. This is not a drain snake similar to what you'd use to clear a clogged sink, but is made for toilets. It's available in hardware stores, and looks like a cane with a hand crank and a coiled cable for snaking. It takes a little getting used to, but works great, and it won't wreck the seal between your floor and toilet, as vigorous plunging sometimes will. It's a tool well worth the small investment. If it doesn't come with an instruction card, ask the hardware person to demonstrate it. Sometimes somebody drops something in by accident and it never goes down, but takes up residence in there, floating in the line beyond the bowl where you can't see it or grab it. Pencils and toothbrushes are famous for this. If you bail all the water out of the bowl, anything floating out of view will fall back into the empty bowl. You may want to try this, too. On your second toilet which demands that you hold the handle down all through the flush, I have two guesses. I think either the handle is worn, or the flapper is worn, or both. They're both very inexpensive and easy to replace. Look in the tank and watch as it flushes - Does the handle pull up a rubber flapper on a chain? Not all toilets use this device, but it's the most common. Take that flapper to the hardware store and get another one just like it. I'll bet that ends your problem. Good luck!