Light blinks, if you mean the Check Engine light is blinking and the starter does not turn then I would look at the transmission Neutral/Safety Switch. The PCM may not be sensing that the car is in park or neutral and therefore will not let the engine be started.
If the starter motor is turning the engine and it is not running then I would see about pulling the PCM code but more than likely you engine needs either a new cam or crankshaft sensor (depending on manufacture) to tell the PCM where #1 cylinder Top Dead Center is so that it can control the engine's fuel and timing.
