As two other folks have suggested, doing an upgrade is not a very good approach.
SQL 2000 cannot be upgraded to anything but SQL 2005. As Grant suggested, the cardinality estimator changed significantly in SQL 2014. You may (will!) experience performance issues with some of your code. Extensive before and after performance testing should be a priority in this process.
You also have very different sets of code for both the OS and SQL. Why leave the old code in place? That is a guaranteed recipe for issues that are nearly impossible to track down.
If you do choose to upgrade as opposed to a side by side migration, prepare yourselves to re-do this in a short period. The volume of potential issues is significant.
Why am I saying DON'T DO THIS to you? Because I've felt this pain many times. As a FTE, I made that mistake myself. That was in the days of physical hardware. You didn't have spare servers laying around. Thankfully, it was not production. As a consultant, I have had to diagnose and correct this mistake for a few clients. Once things got squared away, I made sure that I pointed out to the client that they would have spent far less money had they simply invested in new servers and done a side by side migration.
My question is why? Why is going through multiple steps to do an upgrade your preferred method? If it a financial decision, then you may need to think outside the box.