Is there any way to delete the nonworking setup so it doesn't show up as a choice during boot-up?
Yes, deleting an additional operating system as a choice during bootup is easy. You delete the invocation line of the nonworking operating system from the boot.ini file.
The real issue is whether you actually have multiple installations of the operating system on your system, or multiple "invocations" of the same operating system.
The key to a solution is to examine the "boot.ini" file located at "C:\boot.ini". Normally, the following file attributes are set for this file making it difficult to examine manually: system, hidden, and read-only.
The contents of this file identify the operating system(s) known to your system and where they are located within the file system.
If each operating system invocation line points to a different location for the operating system; either different disk, partition, "Windows" directory name, or all of the preceding; then you have two distinct installations. This sounds like the case you have here, since one works and one doesn't. If true, you may eventually want to delete the directory subtree of the nonworking operating system from the file system to recover the disk space. Don't rush into this. Think about it long and hard. (And back up your important data first).
If each operating system invocation line points to the same location; e.g same disk, partition, and Windows directory name; then there is only one installation of Windows with different options for invoking it.
At any rate, here are some references to look over:
How to edit the Boot.ini file in Windows XP Additional information and help with the boot.ini How to rebuild the Windows boot.ini
