This is a classic symptom of a leaking carburettor float needle valve. Strip & clean the carb - chances are that's all it needs. After you woke it up - and disturbed whatever crud may have been in there after 2 years of storage - something has lodged in the valve seat. While it was running, it was fine, but when you parked it for a while, the leaky valve will let fuel run into the engine where it will dilute the oil. Just change the oil - as long as you didn't run it that way for too long, the engine will be fine. You'll know immediately - because it will either be OK or it will sound like a bag of bolts in a cement mixer.
phil_saunders(a)bigfoot.com
Phil Saunders, March 2011