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By left you mean Port engine and right you mean Starboard ( I'm not being a jerk it matters for troubleshooting).
Are you getting any horn sounds? A 6 second continuous sound is a critical alarm a 6 second intermittent sound is non critical.
Your throttles are DTS, correct? Do you have Axius? Axius Premier? First (respectfully asked) both your throttles are in neutral when you're trying to start? They are somewhat touchy and if not in neutral you will have problems.
On DTS throttles the Port throttle is the throttle that supplies power to both engines when it is used during the "single lever mode". Was this activated at some point?
Many of the DTS throttle modes require the throttle(s) to be returned to neutral before activating the mode buttons and changing modes.