iMac & Macbook Recovery

iMAC:

I am having a few problems with an iMac computer. I can boot up the desktop, and it will reach the grey Apple loading screen. When it moves on to the next screen, the computer will put up a lot of error messages, telling me that there is a boot up error. I have a lot of data stored in there, including some family research which has taken me several years to compile. I need to be able to extract this data from the computer, as it is virtually irreplaceable. I don’t understand what the error messages mean, as they seem to be written in BIOS or another form of computer language. I am anxious in case the system is trying to report an error with the hard drive, because I still want to keep that data which is in the iMac. Is there any way in which I can manage to get the data off of the drive while the computer is failing to boot up like this?

MAC IOMEGA DRIVE:

I have a Macbook with an external hard drive, on which I have stored a large number of photographs and music from my iPhone. The Iomega drive has been in use for over a year, and I am having problems extracting data from the drive now. I am not able to open up the drive and listen to the music files, or even see the photograph files. I wanted to transfer over the iPhotos files from the Iomega in order to back it up onto another flash drive, thinking that this would allow me to protect my information better. However, when I am trying to download the iPhotos file in the Iomega, I get the red circle with the line through it when I try to do the copy, or when I try and do a move. I am not able to create new files or folders on the hard drive, as before. I am almost completely locked out of the hard drive, even though it contains a large amount of data that I want to keep using.