CL30 Captain reported that due to fatigue; lack of compliance during ice checks and deicing led to engine start problems as the engine fan was frozen in place.

Narrative

Removed engine covers and placed freezables back on aircraft. Co-pilot did preflight outside aircraft; I did preflight inside. Temperature was 19°F and windy. [I was] still tired from [the] previous two days [of] flying - 12 1/2 hours duty on Date and 14 hours 20 minutes on Date 1 - that consisted of four flights up and down the eastern US through the cold front; and having the fifth flight cancelled due to duty time limitation. Once aircraft was ready; we strapped in and went over the Before-Start Checklist. Starting the right engine; I heard it spool up and didn't notice the N1 wasn't normal. Starting the left engine; we were concerned about getting the aircraft going so we could get in line for deicing. We were told by the FBO that it was taking 40 - 45 minutes per aircraft and we wanted to make our takeoff time. As I heard the left engine spool up; I notice that an Amber CAS FADEC2 message had appeared and then saw the Amber CAS FADEC1 message appear and dashes. I pointed it out to the Co-pilot and called Maintenance and they told me to shut the engines down; and check to see if the N1 blades were turning. We shut the aircraft down and pulled the batteries; then reconnected them. We called the FBO for a ladder; but they took nearly 45 minutes with no ladder. Co-pilot found a Maintenance Contractor to let us borrow his ladder; at which point we saw that there was about 1/8 - 1/4 inch of ice in the bottom of the cowling. We attempted to melt the ice with hot water and a hot gun; but it was taking a long time and the wind chill factor was in the single digits.Starting the right engine looked normal; I heard the N2 spool up; but didn't notice the N1 indication until I started the left engine. As it spooled up; I noticed both AMBER FADEC 1 and 2 CAS messages and also that there were dashes where the indications would be. I told the Co-pilot and asked him to look it up in the QRH; and then called Maintenance. Maintenance told me to shut down both engines and check to see if the N1 fan was frozen. Once we got a ladder I looked into the inlet and noticed that the N1 blades were indeed stuck to the nacelle. Over the past couple of days; we had been flying in cold weather and long duty days. I had not been sleeping well; waking up numerous times during the night. Date 1 started early and was scheduled for four flights; and one was added late in the day but was cancelled due to delays in getting deiced in ZZZ - which would have put us over 14 hours - which we did anyway due to the delay in getting a ladder so we could put engine covers on at night; in light snow; and with the ladder sitting on 2 inches of ice. I was exhausted by the time we got to the hotel. I ate a late dinner and went to my room to sleep.The morning came early and I felt the fatigue from not getting enough rest. We hustled to get to the FBO in order to de-winterize the aircraft and get in line for deicing and make our departure time. It was freezing cold and windy during the preflight. Putting the engine covers on the night before; I believed that would prevent any moisture from getting into the engine inlets so I did not ask for a ladder in the morning. As we started the Before-Start Checklist; I noticed that I was feeling tired and that my focus was not where it needed to be. Starting the right engine looked normal; I heard the N2 spool up; but didn't notice the N1 indication when I started the left engine. As it spooled up I noticed both AMBER FADEC 1 and 2 CAS messages and also that there were dashes now where the indications would be. I told the Co-pilot and asked him to look it up in the QRH; and then called Maintenance. Maintenance told me to shut down both engines and check to see if the N1 fan was frozen. Once we got a ladder I looked into the inlet and noticed that the N1 blades were indeed stuck to the nacelle. There was a delayed reaction upon noticing CAS messages and other indications. I felt like I was slow in determining what the issue was because I was still tired from the day before. After speaking with Maintenance; we shut down engines and inspected [the] inlets to determine if fan blades were frozen. Wanting to complete the mission and pushing through the feelings of fatigue are traits most pilots share; but when we are assigned additional flights and are tired; we need to remember that safety is of upmost importance and that we are in the best position in determining whether or not to take that flight.