I had the same problem with my inspiron 6000, was quoted ridiculous prices from "reputable" laptop repair shops locally. (I am in Uk, where are you) I found a very helpful company, www.portables.co.uk who supplied 2 new hinges for £25 less than the cheapest repair company quoted me for 1.

I am an engineer and have upgraded/repaired pc's but never laptops, I found this to be really easy and had the job done in under half an hour. 

There are round rubber feet on screen surround which pop off to reveal screws, these come out which lets you remove the surround.

You should now be able to see the hinge and the 4 locating screws, remove these and simply replace hinge, screw surround back on and press rubber feet back into place.

When the hinge is out the screen should be supported to stop it falling backwards and damaging the connecting cable.

If you are unsure if you can do this I would see if someone you know can assist as the prices you will be quoted may be rather high.

Hope it all goes well

Thanks for the quick reply.   My hinge is broken where it connects to the computer itself - not at the cover.    I will try to get some hinges and give it a try.    PS - I spent 30 years with IBM as an engineer, so hopefully I can do it if the parts fit.    Thanks again.