Sorry to hear that you have a Cadet! They are truly a pound puppy of a toilet! The section below is a generic posting I wrote and share with people who have a bad performing toilet. The only thing I would add is that you have a 1.6 GPF toilet and slightly lowering the float on the flapper chain may help somewhat after going through all the other checks. Do not lower it so low that it double flushes.
There can be an obstruction in the trapway such as a "Coney Island Beach Whistle" and the toilet may flush sometimes and not others. Several passes with a closet auger will ensure that the trapway is clear. Use a quality closet auger with a hooked drophead such as a Ridgid or, General brand auger. Don't use an "Econo-Auger", they are useless!
Check the tank water level it should be filled to the waterline or, within 5/8" of the top of the overflow tube. Make sure that the bowl refill tube is in place and operating correctly. It is the tube that runs from the fill valve to the top of the overflow tube. Whenever the tank is refilling water should spray out of the bowl refill tube and down the overflow tube to refill the bowl.
Check the flapper make sure it is the proper one for the toilet and that it is in good condition and working properly. A 1.6GPF flapper installed on a 3.5 GPF toilet will often give a good flush every other flush symptom. It is not said in your post but did your problems start after doing some sort of maint. on the toilet? Also an old flapper will often close at an inconsistant rate varying the amount of water allowed into the bowl per flush.
Clean the ports under the rim of the bowl & the siphon jet. Under the rim of the bowl there are small holes all the way around the bowl. Take a piece of coathanger wire and stick it into each of these holes and wiggle it around to ensure that each hole is clear and allowing water to flow into the bowl. Take a longer piece and run it up through the siphon jet hole (the 1/2" or so dia. hole in the bottom front of the bowl). Any of these holes being blocked can inhibit the fast transfer of water from the tank to the bowl and affect the flushing power of a toilet.
Are you using in tank bowl cleaners? There is an infamous blue glop (Smurf crap) bowl cleaner that is notorious for plugging up the internal water passages of toilets. If you are using this discontinue use immediately and hope that it will clear out. This stuff has ruined many toilets!
After taking all these steps if the toilet still is not flushing well replacement may be your best course of action. You may do the bucket test to see if the problem is in the bowl or the trapway. Do you have a 1.6 GPF or, a 3.5 GPF toilet? Fill a bucket with the amount of water that your toilet is designed to use. Pour the bucket into the bowl as fast as you can and the toilet should flush properly. If it does the problem would be in the tank to the bowl passage way causeing the water to enter the bowl too slow to allow a strong flush. If it does not flush the problem would be in the trapway of the bowl.
That said you may want to hire a pro to check it out for you to ensure the unneccessary replacement of a toilet. If replacing a toilet I would highly recommend the installation of a Toto Drake. It is a great quality toilet that will retire your plunger for sure!
Before purchasing a new toilet I would encourage you to check Terry's report on low consumption toilets. I would also avoid "pressure assisted" toilets as they are noisy and when repairs are needed can be quite costly.
My recommendation of the Toto Drake as a replacement is based on several reasons. The in the tank parts are not expensive and are commonly available. The toilet is rated at 900 GmPF and as a rule any toilet above 6 or, 700 GmPF will prove to be a pretty reliable flush in most cases excluding medical conditions that challenge any toilets flushing ability. The quality is high at Toto, I have been installing them as my toilet of choice when I provide the toilet for over 5 years now and have never had a callback on any of them! I have even installed tham in commercial applications and have satisfied customers there as well. You know public restrooms can challenge any toilet! Infact I have had several business owners and managers call wanting one of them "Super Toilets" installed in their own home after seeing how well they performed.
When the Toto Drake arrived it propelled every other manufacturer to send its engineers back to the drawing board to come up with a toilet that flushed as well as the Toto Drake after years of insisting it couldn't be done. They did pretty good at copying the large dia. flush valve, enlarged, rounded curve trapway, and glazing the trapway to make a toilet that flushes "as good as a Toto Drake." Why buy a copy when you can own the benchmark!
In fact Toto has upped the ante and is now manufacturing the Eco-Drake which is HET rated with a 1.28 GPF gravity flush! This toilet flushes the same 900 GmPF as the regular Drake but does it with a 1.28 GPF gravity flush when most other manufacturers went with either a dual flush (#1 button + #2 button for different flushes) or, a 1.1 GPF pressure assisted flush.
Hope this info helps you out!