Just like wattywatts stated I can not help but feel random shots in the dark are what you are going to receive here, would not be the first time I was wrong though! However, in light of this I think a little more information might help, such as posting the crash report so that more adept users can aid you.
Quote: "Something has happened to either my Windows XP, DBPro, DirectX"
Firstly I could not say what state XP is in with regards to updates as I do not have it. Either you have automatically updated something or you have done something manually, or perhaps you have some sort of virus though it would be inexplicable to me as to why a virus would target dll's of the 3D nature just in DBP's installation. The only issues I have ever had with DBP when its been a DBP related issue in the past has been with plugins, for example I did not properly follow IanM's instructions for his plugin and ended up going around in circles because of it, getting my wires crossed being unaware that some of his dll's commands are replacement commands for some of the 3D commands in DBP. In terms of direct x, well there is no automatic update for that I am aware of so in this case you would have had to change something. As wattywatts stated uninstalling DBP should be done along with removing any residual files left in the install folder just in case there is a plugin you have forgotten about still installed - I am unclear as to whether DBP uninstall deletes the folders as well.
Quote: "or perhaps Microsoft .NET"
This is not a dependency for DBP so I do not see how that would be of relevance, unless there is some factor my meagre knowledge is unaware of which is of course entirely possible.
Quote: "Whenever I compile an app with no 3D commands it seems run fine, but if I include any 3D command, it compiles but crashes when I run it."
This did make me think about what I have already mentioned regarding IanM's matrix1utility commands. There also remains the possibility that perhaps you have recently installed either manually or by automation a new driver for you hardware or maybe an old one or the wrong one by mistake. If that turns out to be the case you can try rolling the driver(s) back. Does other software that uses direct x 3D run fine? Knowing this might help others determine the cause.
That is all I can think of at this time so best of luck with this