I feel like there are a lot of things that need to be addressed other than your question itself. Please bear with me, you'll come out better in the end.
I had a Windows 2003 Hard Drive on my server and it went bad so I installed a new clean hard drive and installed Windows 2008 R2 on the new clean drive.
You should have backups for any production system. This should be a #1 priority.
In addition to that, you should use some level of hard drive redundancy. RAID 1 will take two disks and make them mirrors of each other. If you have two 300GB hard drives in a RAID 1, you'll only have 300GB of space available, but if a hard drive dies, your system will continue to function until you replace the drive. Keep in mind that RAID is not a substitute for a backup. You should have both.
This question has a lot of good information about RAID, what it is, what it does, and what it's good for. I really recommend reading it.
I moved the old 2003 drive to be used only for general storage on the same computer.
When adding disks to an existing install, which is basically what you're doing here, you should wipe them if they previously had an OS partition on them, precisely so that you avoid hiccups like this.
I need to know how to remove any old code that keeps this old drive as a bootable drive.
Windows server 2008 and later use BCD instead of boot.ini. You'll likely need to use the BCD commandline tools to remove the 2003 server from the boot order. The documentation for
bcdedit.exe is here. It has everything that you need to find, enumerate, and remove the 2003 Server entry from the boot menu.
I still want to use it as a secondary drive just dont want to have any boot code on it.
You should really consider adding it as a mirror (RAID 1) of your current OS drive.