All the above are helpful hints but it seems the most obvious little things are usually the issues. We see 1000's of mowers a year and most of the time you will find a simple solution. I have come up with a diagnosis tool that might be
helpful to you advanced-power-equipment.com/lawnmowerdr.htm.
Some issues on this forum seem to be over thought. Yes, carburetors are an issue, some can be dealt with but most need to be replaced if it is truly a carb issue. Check the easy stuff first!