Is the technology currently in place to launch a manned mission to Mars (and is it thus just a resource constraint that's preventing such a mission from occurring), or are there still other technologies we need to develop for this to be feasible? If so, what are they?
There is a fellow by the name of Robert Zubrin who has made a case by which humans could travel to Mars within existing (actually long existing) technology, and within NASA's existing budget.
If all his facts are correct, then there is no technological or financial barrier to landing humans on Mars.
Given the money and the time, most of the required technology is already available. The one exception is that we do not have the technology today to land very large payloads on Mars, specifically in the 20 tonne to 40 tonne range, as is required in published human Mars mission architectures. This report states:
These interactions are most evident for the development and evolution of human class EDL for Mars. The approach that will be used to land tens of metric tons of payload on Mars is not known today, and cannot be known purely through paper studies. Only through technology development can the large uncertainties that exist today be reduced in the design of such a mission in order to begin to converge on the most cost effective and reliable combination of systems.