You may experience no mountable files during booting of Mac which is why system does not boot properly. In fact Mac uses DMG file in order to save precious system files which ensures proper functioning of the system. Meanwhile DMG gets damaged in some point which cause no mountable files. Since users certainly lose the access of Mac at this juncture therefore it is must to resolve this issue as the earliest. Losing the access of system is pretty annoying obviously and no body wants to be in such catastrophe. Fortunately using disk utility one would able to repairing disk permissions which is helpful and may resolve no mountable files. But if you succeeded to overcome this problem then reinstall OS X.
However for doing so you may face file loss crisis which needs to be sorted out and if there is previous backup available then it is not so hefty task to regain lost files. In lack of backup it is strongly advised to use third party Mac Data Recovery Software for restoring missing and inaccessible Mac data efficiently. You no need to wander about restoring of lost file after having this excellent application. So resolve no mountable files now.