good advice above from Anderkart and others.
PLEASE: wear safety equipment when handling a saw. Not trying to be a safety nazi, but chainsaws are very dangerous esp. one that's working intermittently that may grab/cut/slack off etc...
a really good site to search thru is ArboristSite.com for help
If you have a compression tester, you need to check for compression, and do a leak down test. There can be lots of places for air to leak in and compression to leak out...
It's down to basics: air/fuel/spark. You say it's got plenty of spark, appears to have plenty of fuel (is it fresh?), so that leaves air
Air:
intake: (seems to be clean/working), may need a kit as stated above, but runs up under no load "ok". Are you running it with an airfilter? is it clean/new etc?
exhaust: you say it may be plugged, you can also heat and use plyers to uncrimp folded mufflers to clean it out.
compression: you need to test for compression and leakdown
I'd doubt the timing was changed unless someone tried porting the saw prior to you working on it. "Most" saws are just used by home owners and neglected in maintenance.
Don't run it long without the muffler, or without the chain on it you may add damage to the saw.
and FWIW: $10 isn't enough to take the time to make the vid and ask the questions you've already asked online. A regular saw shop would charge him $50/hr min, +parts, so IMHO your time should be worth $25+ at a min, but that IS a way cool siren you got in trade, so it's a wash
