Yes, so long as the invention satisfies the conditions for patentability, i.e. the invention must be novel, non-obvious, and have some utility. The fact that the constituent components of your invention are already patented does not necessarily prevent you from obtaining a patent, but may well play in to the obviousness analysis if the Examiner were to cite two references against you, for example.
You would be wise to speak with a patent prosecution attorney for a few minutes and discuss specifics. That discussion will likely be much more worthwhile for you than answers to this rather abstract question.
The answer is a definite maybe. Even if it was known to combine those elements to make a toy gun, if those elements are combined in a different way than previous toys (and the legal scope of a patent is based primarily on the claims in the patent), then your invention would be novel, which would meet one of the requirements for patentability. But, if your new combination would have been obvious to "one of ordinary skill in the art" (such as a typical toy maker) at the time of your invention, then it would not meet another requirement for patentabiltiy. Thus, patentability requires that the invention must be both novel and non-obvious.
This is a highly simplified analysis of patentability, and is not intended to provide a legal opinion about the patentability of your proposed combination.
This answer is for informational purposes only. It is not intended as specific legal advice regarding your question. The answer could be different if all of the facts were known. This answer does not establish an attorney-client relationship.
My colleagues' answers are correct that it is a fairly complex analysis of the existing patents and products to determine whether the new product meets the standards of novelty and non-obviousness (35 U.S.C. 102 and 103). However, there is a secondary consideration that you may not have considered.
Patent rights are what are referred to as negative rights, not affirmative rights. Patents give the owner the rights to stop others from making, using, selling, offering for sale or importing products that infringe their patent. Nothing in the statutes states that you have a right to make your product once the patent is granted--in other words, just because you can get a patent doesn't mean you can make your product. This means that just because you have a patent doesn't mean that making a product in accordance with your patent is legal. For example: Say your product includes parts A, B & C and part A is covered by a valid and enforceable patent. In order to make your product, if you manufacture Part A (without obtaining a license from the patent owner), you are very likely liable for patent infringement. You could purchase Part A and then include it in your product, but you will likely not be able to manufacture that part yourself without permission from the patent holder.
You should, of course, consult with a qualified and experienced patent attorney to discuss this matter in more detail. However, this is one consideration that a lot of new inventors overlook and it is something that should be reviewed and understood before spending a significant amount of money on getting a patent.
It is possible, but probably not likely. Can you identify some new functionality or some unexpected result achieved by the combination?
A Supreme Court case a few years ago has made it very difficult to patent a combination of old elements. Sorry for the bad news!