Have you checked your fuses in your engine bay? Start there, make sure those are good. From there...this is from another thread that had your issue

This was a very strange issue. To summarize, I pulled my car out of the garage to clean the garage. When I was done, I pulled the car back into the garage. This was for Thanksgiving mind you, so a bit chilly here in Colorado. Six hours later I went to start the car and it would not start. NO clicking sound, NO dead battery. The engine sounded like it wanted to turn over but didn't have the juice to completely turn.

Here is a list of things I did and checked:
Attempted a Jump from a friend (so many people suggested bad battery or alternator) - No Go
Checked the ground - Ground was fine
Checked fuel pump fuses - All good
Checked spark plugs - All good
Tried about 10 times in a month's period to get her started - no go

This lead me to believe it was a fuel line or fuel pump issue. Being that the pump is inside the fuel tank, I decided to have my car towed to the dealership (Car is still under factory warranty). I should have done this or called and talked to an actual mechanic in the first place there. The service lady initially told me dead battery... again NOT the issue!

The car was at the dealership for 10 minutes before they called me and told me my car was up and running! The issue..... Engine was Flooded!!! The reason they knew is from the moment I got off the phone with the service manager? My story, pulled the car from the drive way to the garage in cold weather for a 10 second period of time. They have this happen alot here in Colorado and cooler climates. They themselves will pull a person's car around for pickup, the owner will go out to their car to start it, and the car won't start after just being worked on! The short time period that the car is running and turned off floods the engine.

The solution: I am quoting the mechanic here " Press down both brake and throttle as far as both will go, then press the start button/turn the key" This forces air through to "unflood" the system. After a couple of seconds, the engine will turn over

I hope this helps anyone else looking to see why their car mysteriously won't start. Message me if you have questions!

 

Try some of the things in this video link above. I would start with making sure your battery is connected well and is working properly. I know you replaced it but maybe it is draining somehow and doesn't have enough juice to turn your engine over. One thing you can try immediate is to put the car in neutral and try starting it to make sure it isn't something with the sensor that tells the car it's in park.

 

Might be a bad brake switch. Try and swap that out, they are at most $50. Had a similar issue in the F.

 

Yes, look like your brake switch is not working properly

 

 

 

In your video the green light comes on the switch, this says the brake is being depressed to activate the start sequence. So that is not it.

Does the engine actually spin / crank over?
If yes, now check for fuel and spark.

If no, now we dig into what is inhibiting the starter.
Make sense?

 

Press and hold the brake and gas at the same time as hard as you can....push button after about 10 seconds

 

Believe it or not I had a similar issue with our '08 IS250. In the process of determining that the fuel pump was bad, I replaced the battery as a first step. Car wouldn't crank or even make a sound - just like yours. I had no idea what it was because even though the first battery was bad it would attempt to turn over.

I finally narrowed it down to this: when you replace the battery you need to close EVERYTHING - doors, hood, trunk - and give the system time to reinitialize. After I closed everything and stepped away from the car for about 10 minutes and came back it cranked!! Also, don't forget to reinitialize your windows...go to each door and lower them halfway and then raise them.

 

 

 

You should hear the fuel pump prime just before you start the car. Try this: disconnect, and then reconnect, the battery. Be sure the hood and all doors are closed. Wait 10 min then try and start the car.

 

Just and update... the car still isn’t running. The last time I checked it I heard the fuel pump turn on so I know that’s not the problem. I tried to unfold the engine by doing the steps still to no prevail. Still will not start. So this morning, I went to to go fool with it and the battery dead giving it should be with the number of times I tried to start it. But this strange noise was coming from it and I don’t what to call it. Can anyone help me out? Here’s the link

 

Sounds like a relay clicking noise not sure. See if you can find the EFI relay and pull it.