I doubt that the dropping of the remote could, or would have done anything permanent as as soon as one turns off the unit, or at least removes it from the wall power it will reset. So you might like to try that first. Also remove the batteries from the remote and this will set it all back to factor fresh. Now try the TV set again, DO NOT use the remote use the actual buttons on the TV this time to remove the remote from the equation.
Now if it goes all good, NOW try the remote, it may just be that. Dropping may have damaged?
OK if it doesn't work, and still exhibits the same symptoms, then these symptoms are ones i have seen many many times, and it means that your Power Supply has sensed some sort of fault within the set, and in an effort to avoid a fire and explosion or indeed both it shuts down the TV so it cannot be used until repaired.
Rear projection sets are very prone to faulting, due to their design. I am sorry to say but professionally I know there is no easy home fix sorry.
What you need to do is it is my professional opinion you should take your units to their manufacturers approved service center, you do this by contacting a, local or head office, of your unit & getting referred to an approved service center, NOW this is just SO important, even worth the extra to ship it, you see, at those places, the Engineers, are trained on the equipment you have, they usually have parts on hand, and do the job quicker. Anyway do that and get a "Quote". before allowing any work to commence. This way, at least, you'll know weather to repair or replace.
Please find below whats called a training manual, this is whats used to train the engineers to be able to troubleshoot and service these sets, have a look just how complex and difficult they are to understand and service. just so you can get an idea of what goes on.