I realize you are talking about a DVD BURNER inside a computer, but I think the technology may be similar to problems I and many others are having with LITEON DVD recorder products made for the TV sets.
My LITEON DVD RECORDER VHS UNIT 5005 series does this. It usually happens with a disc in it, when it decides it is an invalid disc, which it isn't. It seems to loop between the preparing stage and the reading stage. It will not open. I actually had to pull the unit forward and tip it down and shake it. If you try to pull it out with force, it will break the front panel, so don't force it. I had to gently shake it in this position while I turned it on and off and on and off with the power cord. It finally released. If it opens grab the drawer so it won't close again. You should use a cleaning disc at this point. After that I changed discs but it only will take a RW disc now. Almost all other media says INVALID, but it works with the RW discs, so far. I have read that LITEON recommends a firmware upgrade, but I have also read that the upgrade doesn't fix the problem and sometimes causes more issues. It also seems that dirt and dust gets into the laser area, and that might be one of the causes. Once I got it open I grabbed the tray so it wouldn't close and put in the cleaner disc, and it read that and I ran the cleaner 3x.
I also have the INVALID disc issue on my other LITEON PRIDUCT LVC 9016G, but the tray doesn't stick. It seems that both products have lost their ability to read most discs. And after a while if you leave a disc in the unit NOT FINALIZED it says it is INVALID and will no longer allow you to finalize or read it, so you lost the info. I usually use SLP, and I think perhaps it wants to go no more that SP or 4 hours per disc rather than six. If I get to the 4th hour and above it may deem the disc INVALID.
I have no technical background, but I am a psychology major attempting to analyze this sick group of LITEON machines.
If anyone has any actual technical info that can help these machines start working let me know. OR ELSE I AM GOING TO HAVE TO SPEND A BUNCH and buy PANASONIC next time. They don't have all the bells and whistles, but they seem to work!