Eclipse 500 pilot reported a rejected takeoff due to the engine not running.

Narrative

Takeoff abort due to one engine not running.While commencing my takeoff on XXR at [taxiway] 1; I noticed the airplane was not accelerating normally and also pulling to the right. After ~1200' at 60kts I retarded the throttles informed the tower and aborted the takeoff. Initially I suspected a mechanical problem of some kind; but as I exited the runway at 2 (~3500)'; I realized that my right engine was not turned on. After starting the right engine; I taxied back; took off normally and completed the flight uneventfully.I had landed on XYL 30min earlier; but the winds shifted so much during fueling; that I felt it was unsafe to start the engines with a tailwind. I then pushed the plane forward (with the help of the wind) and turned it a bit to alleviate the direct tailwind. I started the left engine; did my safety checks and then taxied to the runway. Possibly I was worried about blocking the taxiway or I just wanted to get underway before the weather worsened. After calling for my release I noticed the 'Takeoff Config OK' message was not present. I checked the items that normally cause this error: engine T/O temp; flap position; trim; parking brake; and the door but all were normal. I even advanced the throttles as this normally leads to a loud warning highlighting the incorrectly configured system; but there was nothing. I decided it was a computer anomaly and believed I had a perfectly good airplane (it had just landed normally after all).As I accelerated down the runway (with no CAS messages) I quickly determined that the plane was not developing full power and aborted the takeoff.In the future I will not 'call for release' until I have 'Takeoff Config OK' displayed. I also think the software should be modified so that ALL configuration items generate a warning CAS if the throttles are advanced. The two missing items are: Flap Position matches flap setting; and Both engines are running.