If it flushed ok with the bucket test, it most likely has clogged ports. The ports are located under the rim. You can use a small mirror and clean these out with a wire coat hanger, screwdriver, or a nail. You should also clean the main port or “jet” at the bottom of the bowl as well. After these have been cleaned, pour some vinegar into the tank slowly while holding down the handle. Vinegar breaks down calcium and lime deposits that have accumulated in your bowls ports. If you are on well water and have hard water stains in your bowl, this is almost a guarantee that your ports are slowly closing off. Also, if you have ever used any sort of blue tank tablet, the remains of it may be clogging one or more of your ports. This can be a little bit of a problem, since it will just move every time you attempt to poke at it. Don’t worry, it will dissolve in a few MONTHS.
If it did not flush when a pail of water was dumped down it, you will have to address the blockage. The easiest thing to do will be to try and plunge it a few times. Be careful about excessive plunging though, as this could actually cause the wax seal to leak. If the plunger is unable to clear the problem, then you will have to use a toilet auger. If the closet auger is still unsuccessful, it most likely means that you have a blockage further down your drain system. This will require the toilet to be pulled and the drain to be snaked. This is best left to a professional.
One more possibility could simply be that you have a very poor quality toilet. Before the ’50’s, toilets used as much as 7 gallons of water per flush! By the end of the ’60’s they were using about 5.5 gallons per flush. In the ’80’s, toilets were now using only 3.5 gallons per flush. In 1995 The National Energy Policy Act (H.R. 776) went into effect and mandated toilets to use no more than 1.6 gallons per flush. Unfortunately, almost all of the early 1.6 toilets were terrible flushing units, especially compared to all of their earlier counterparts. You may have one of these.
A few more thoughts and suggestions: 1. NEVER use drain cleaning chemicals. These are only band-aid solutions that will only clear minor scum, but will not remove the actually blockage. You should always just hire a professional drain cleaner (we DO NOT clean drains by the way) to clear your line properly. Ancient mummies are still found with hair on their heads, do you really think chemicals will dissolve it in your drains? If it did, it would also be eating away at your drain lines, which would be even worse I would imagine. 2. NEVER use a tank tablet. That pretty looking blue stuff has bleach in it, which eats away at all of the plastic in your tank and can clog your ports. 3. There are some very nice 1.6 gpf toilets available now days. Most of them will flush better than the 3.5 gpf. There are also dual flush types, that will flush 1.6 or 1, and there is also a 1.28 gpf. 4. DO NOT put chemicals in your drains. Did I say that already?