I read through this post, and I wanted to suggest one other thing on top of the impulse line, and fuel line and filter.
Pop the carb off and make sure the intake flanges were put back in. If a dealer rebuilt the carb, I have seen once or twice that someone had said they put a kit in the carb, and the saw wanted to run good, but was acting funny, and they were at a loss. It was dismissed as a bad carb. So, a new carb was bought, and when the one that was rebuilt was removed, it was found that the inner and outer metal flanges were missing off the boot. It happens, and I have done it once or twice while kind of rushing to get to the finish line. That will create a non rigid and secure mount of the carb to intake boot area, making enough of an air pocket to really mess up the air fuel fix. Also, check that boot. Fire her up and spray the boot with some starting fluid, or brake cleaner is better, or carb cleaner. Just enough to see if the saw stalls, or races slightly. Of course another thing, although I don't believe it is the problem, is give a quick spray to the base gasket area. Maybe not sealed up there.
With the wt carbs, when I rebuild them I am about 50% successful with them. Half of em rebuild really well, the other half, I have to adjust em quite a few times to finally dial it home. And sometimes I find my final settings to be a half a turn almost past factory specs on the low. High is often fixed, non adjustable, or if it is, never seems to need too much change. Those little diaphragms are so sensitive as well. The smallest little non visible pin hole or tear from handling it too hard can wreak havoc in the end.
There's a seller on eBay selling new genuine Walbro wt carbs. I picked one up for 40.00, and it came even with the stihl plate on it! They are 44.99 now, but they aren't aftermarket, they are genuine Walbro. It works awesome. It came not pre set, so if you buy one, dial it to one turn on both screws. But it's a high low adjustable.
I hope you didn't pay too much for the coil, and that it was an Oem one. I have seen aftermarket coils not work right out of the package. I have 3 or 4 coils for the 026 here that work, they are used, but Oem. If there's an issue with the one you bought, let me know. It may be a good idea to see if your flywheel is ok. I have seen a flywheel with a bad scratch or mark/ding on the magnet before, which upsets the spark. Very rare though. That took a lot of testing different parts before I found that problem.