Okay, I forgot that the Startup Manager procedure only shows both OS version if they are installed in separate partitions.
Try this: Start in "Safe Mode" by holding SHIFT during startup. This disables extensions but should leave you being able to get to teh Startup disk control panel, NOTE: A safe mode boot takes longer because the system does some checks and clean-up during Safe Boot.
It could be that your internal Backup battery ("Pram" battery) is dead. That could make the computer "forget" where its startup volume resides. You can overcome this by either starting from a System disk (will give you access to one of the startup control panle option, which is on every Apple system disk.).
You can also try "zapping the PRAM" by restarting and then immediately pressing and holding these four keys:
command
option
p
r
Continue holding until you hear a total of THREE startup chimes, then let go the keys and let normal booting continue. This probably requires an Apple keyboard; a third-party USB board may not hav the proper key assignments until after the system loads.
As we are getting into more complicated procedures, it would be a VERY good idea to tell us whether this iMac has a tray-loading optical drive or a slot-loading drive. Also please post your processor speed.
PRAM batteries are cheap if you get them online:
3.6v Newer Technology Lithium 1/2 AA PRAM Computer Clock Battery
That one works with all but the very first tray-loading iMacs, and you can access through the RAM door on the bottom of the computer. You may need a non-conductive pair of forceps to reach it.