I struggled with my 028 super for a little while. It would run very erratically, especially at idle, but mine would at least always start so not sure this is going to be any use... but given you've ruled out the obvious things have you thought about bad crank seals? Apparently prone to going on the 028 and possible if they leaked badly enough the saw might not start at all (assume lack of crankcase vacuum / no impulse to pump fuel as you are suspecting). It's a bit fiddly to change them but their cheap and doesn't take long. In your position I'd just replace them or if possible rule that out with a pressure /vacuum test before admitting defeat.
As for testing impulse... I've not tried it myself but I've read somewhere, a long time ago, that putting a blob of grease on the end of the impulse line and pulling the saw over is a quick and dirty way to test - if there is impulse the grease will be drawn into the hose.
