This might sound like a dumb question, but are you sure you installed the new hinges correctly?
I'm thinking that if you installed the hinges with the hinge pin on the wrong side of the hinge (relative to the door) the motion of the hinge could interefere with the raising of the door.
That said, after propping up the garage door in it's fully partially open position with a piece of lumber or something, I'd go inside the garage and see if any of the wheels on the door are hitting something. Or for that matter, if anything on the garage door is hitting something to prevent it from moving further upward.
And, failing that avenue of investigation leading to a solution, I would phone the Holmes 1-800 customer service phone number.
If this has happened to you after replacing the old hinges, it very well may have happened to lots of other people after replacing their hinges, and Holmes would have investigated and found out what was causing the problem.
They'd be the people most likely to know what the problem is because anyone else in your situation wouldn't have gone online to find a solution. They would have phoned up Holmes and asked "What am I doing wrong here?", "Why doesn't my garage door work properly with your new hinges?".
I hope you didn't throw the old hinges out yet. You might just need to reinstall them to confirm the door works properly with the old hinges re-installed.