I had a look at the technical service bulletins (TSB) from Chevy, and there is one that may be related to the P0300 and P0700 codes. This is going to need to be checked out by an experienced mechanic that can look into these codes, this bulletin and come up with the proper solution, this is not for the inexperienced.
TSB#05-06-01-030D: 1.6L Intermittent Misfire During Deceleration or Steady State Highway Driving After Cold Start with DTCs P0300, P0700, P1781
and/or U0401 Set (Replace Valves and Valve Stem Seals) - (Sep 12, 2007)
Condition:
Some customers may comment on an engine misfire on rare occasions. Typically, misfires related to this valve sealing concern will be very intermittent. The intermittent misfires may or may not be felt by the driver and they will normally occur during engine warm up, deceleration, highway driving, wide open throttle acceleration, and/or uphill driving. Additionally, DTCs P0300, P0700, and/or P1781 (2004 models)/U0401 (2005 models) may be set. If a brief engine misfire occurs, it is possible that a P1781 or U0401 DTC may set without the presence of a DTC P0300.
Cause:
The engine misfire may be experienced due to a valve sealing concern.
