|What are you trying to install on C, and from what - a CD or DVD, or from the hard drive, or ? |
If the external drive is not plugged in and Windows is looking for something on logical drive E while booting normally, then Windows must have previously been set up to load something that's on E. If you're no longer using whatever that is, connect the external drive, and if it's assigned E, Un-install whatever program created whatever wants to load, in Control Panel - Add or Remove Programs.
The drive letter assigned to an external drive partition isn't necessarily the same every time it's plugged in. Windows assigns drive letters to partitions on external drives and other removable drives according to which drive letters are available when the drive is plugged in, the lowest available drive letter, alphabetically, first.
E.g. if you unplugged the external drive, then plugged in a USB flash drive, if the first available drive letter is E, the USB drive will be assigned E. If you then plug in the external drive, if the first available drive letter is F, it will be assigned F, not E.
If Windows is set to load something that's on E, it's likely not going to find it on the USB flash drive.