Most likely your insurance company will go after your former landlord's insurance company for reimbursement. It is called subrogation which is a very common practice in the insurance business. I clerked for a real estate insurance attorney while I was still in school many moons ago. You should be able to get your deductible back but it is not at all a fast process. It could take months or years. Contact your agent about that. Unfortunately all insurance can do for you is give you money for your losses. You will have to find the replacements for your D & D collection on your own.

Here is a fairly good discussion of what legal negligence is: http://en.wikipedia.org/wiki/Negligence