Imac will not boot up - help!

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Following on from the thread about inheriting an old iMac today Ive run into a major problem. I was using it online with no issues (its been flawless since I got it) when all of a sudden whatever site I was on wouldn't load the link I was clicking on. I initially thought my internet connection had dropped out but checked and all other devices were working. I just decided to reboot the machine. When rebooting I got to the apple logo with the bar beneath showing progress, all going fine when after abut 10 seconds it shut down. Screen goes instantly black. Every time I switch it on this now happens.

I have tried command R and I can get into the recovery system but that's about it. Even trying to do a fresh install runs into issues because it says the disks are locked.

Does anyone have any help or advice they could offer. Im not hugely technically minded with this sort of stuff. Would like to avoid a reinstall if possible but will do it if required.

 

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Thanks for all the suggestions. Only command R seemed to work for me so options were limited. In the end I just erased the disk and did a fresh OS install which seems to have worked. Fortunately I didn't really have anything too important on it so haven't lost anything of value. Needless to say that its prompted me to sort out automatic back ups etc and means I don't have and files cluttered on it now either. Might as well make the best of it.

 

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Time Machine, it couldn't be easier, especially on an iMac. Just plug a USB hard drive in, set it up and forget about it.
For boot and braces, have a second hard drive connected and run a nightly backup using either SuperDuper! or CarbonCopyCloner.

I do both!

Yup, got Time Machine all set up now which was something I should have done at the very start, wise after the event as usual!