The optical drive will just slide out. There should way to eject the whole thing without cracking open the case (consult the manual). Sometimes there is an eject button/lever or a screw that keeps it from sliding out.
I was thinking of just the external ports: if you have anything plugged in, disconnect it. (printers, peripherals, mice, game controllers, external storage, and so on)
You are right though, if the problem is inside the laptop, there is little you can do.
Specifically, I have had a CD drive fail in the past and it manifested itself as a really long boot time. When I removed the device the boot time was back to normal. I have had the same thing happen with a printer, and an internal storage drive.
You could also run some hard drive diagnostics (consult the manufacturer of your hard drive) in case it may be the component that is failing.