Okay, Let's start with a couple of questions, and please don't be offended if they seem over simplified.
When you replaced the carburetor, did you buy OEM (Zama I believe) or one of the knock off's?
A compression test is necessary, are you able to preform one and let us know the results? Around 150 pis is great. 110 psi and under is considered the problem area (at least in Stihl's opinion) Even with new rings it could still be low if the cylinder is out of round. Why did you replace them? Old rings scored? Cylinder wall scored?
If the plug is not getting "wet" when attempting to start it, then fuel delivery is the problem. I believe that this is a ported, 2 cycle engine. There are several things that play into fuel delivery. Compression is one of those, kind of. Not cylinder compression, but crankcase compression. When the piston travels up during the compression stroke it creates a negative pressure area in the crank case. Atmospheric air is then drawn in through the carburetor picking up the emulsified fuel mix and flowing into the crank case (that is why you only see the bottom of the piston on the intake side of the cylinder, buy design so fuel goes into bottom of crankcase) Then on the down stroke of the piston, the fuel mix in the crank case is pressurized causing the fuel mix to escape to the top side of the piston via the ports in the cylinder walls. That is the quick generic version anyway.
Now if the engine is not capable of creating enough of a vacuum to draw fuel in, it can certainly mimic a carburetor issue. Assuming that the carburetor is a new OEM replacement that hasn't been altered or disassembled, then it's likely not the issue.
Here is a list of things I would check.
1. Fuel lines attached appropriately. Line with filter to inlet side of carburetor, return line to tank attached to primer assembly. Air filter new? I guess I am assuming you are trying to start it with out one installed while working on it, but a clogged filter will inhibit fuel delivery as well.
2. Compression test on top side
3. Check the intake gasket and intake manifold to make sure the pulse or impulse path is open. Should be a little hole in gasket and manifold that need to open and aligned. Helps deliver a pulse of air to the fuel pump side of the carburetor that, in turn helps delivery fuel to the engine. Also check for cracks in the manifold. I can't tell you how many I have cracked from over tightening the screws.
4. Remove the muffler and pull engine over several times and check the plug to see if wet. I have heard of some new new CAT style mufflers being faulty when new and not allowing the air to escape through it. If the engine can't exhale the exhaust, then it can't inhale air and fuel mix.
5.One of the most important tests on 2 cycle equipment that gets overlooked all of the time is a Pressure and Vacuum test of the crank case. Several years ago, I learned through a lot of wasted and unpaid hours of labor, to add this test to my diagnostic list on all 2 cycle equipment that I work on. If an air leak is present in the crank case, it will mimic carburetor problems to the point of insanity. ( HaHa ask me how I know that)
Pressurizing the crank case will highlight any air leaks present. I.E. intake manifold, cylinder gasket, crank / oil seals (these are often the problem) sometimes even a hole in the casting. Imagine the piston traveling down to pressurize the crankcase and shoot the fuel mix up the ports. If all the air getting compressed just shoots out of a failed oil seal then the fuel mix can't be forced to the topside of the piston. Sometimes an engine will pass a pressure test, but fail a vacuum test, so both are necessary. When pressurized the lip on the oil seal is forced on the crankshaft making it seal. But during the vacuum test that lip may pull inward allowing air in. If so, then this suction will also happen during the compression stroke when the engine is trying to create a vacuum in the crankcase to draw air and fuel through the carburetor. Air follows the path of least resistance. If an oil seal is leaking it will draw from there first instead of pulling through the carburetor.
All of that may sound more intimidating than it really is. A 6 or 8 dollar oil seal has driven many of us crazy, probably more than once (at least myself anyway)
Before I got the 'appropriate" tools I would go to the hardware store and get some sheets of rubber gasket material. Cut a triangle shaped piece that will fit between the muffler and cylinder, and one that will fit between the carburetor and intake manifold. Put the piston to top dead center (TDC). I used the adapter for my compression tester to screw into the spark plug hole. It has a hole in it that will accept a piece of fuel line. Run a piece of fuel line into the hole and thread the adapter into the cylinder. I have a hand pump pressure gauge that will plug onto the line. I have heard of guys using a compressor for this, but warn against it. More than 7 or so PSI and you risk blowing out good seals. I usually pressurize to approximately 6-7 psi. Then with a spray bottle filled with soapy water, spray around all possible points for leaks. Look for bubbles, and fix leaks accordingly. Vacuum test is almost the same. I use a MityVac hand pump. Follow the same steps with out soapy water, don't want the engine to inhale any. Set vacuum and see if it holds. One thing to remember, if the vacuum holds, rotate the crankshaft through several positions and see if it holds. Sometimes vacuum leaks are positional.
Sorry for the information overload. I hope some of it helps.