Picture is dark with a green outline on objects.
http://www.eserviceinfo.com/index.php?what=search2&searchstring=Hitachi+57F500
Above is your service and repair manual. to download and print out, you will need this if you decide to DIY (NOT recommended), and in any event the repairer will be extremely appreciative of a copy, and it will expedite any repairs that need to be made. (A good engineer should have one at hand, however it can never hurt to provide it.)
Now whenever a screen is dark etc, we must always suspect that the Voltage that is suppling it is too low, for whatever reason. Often it is because the SMPSU is faulty, or a component(s) are faulty, and drawing too much current, and thus dropping the Voltage. The fact it get darker indicates that the fault worsens with time and heat no doubt. (may be finadable with freeze spray?)
RP TV's are notoriously difficult to repair due to their basic over-complexity. We engineers quite dislike RP TV's and I for one would NEVER recommend that one ever purchase one, for a myriad of reasons. Plasma or LCD LED TV's in the larger sizes are a much better option, and if one must have a GIANT screen, then a good projector is a better bet.
I'm my professional opinion the absolutely best thing to do, is to contact Hitachi, either the head or a local office, and ask them for a referral to an Authorised servicing center. Either take it to them or ask for a service call. Now when in contact, ask for a "Quote" for the repair before allowing any repair work to be undertaken. This way you can then make an informed decision as to what to do, repair or replace. (Often clients prefer to put any large amounts of monies, that would have been outlaid on any repairs, towards a new/used modern set, with a warranty)
You see these days with sets such as this often the cost of repairs can quickly approach the cost of a NEW comparable unit, with a warranty. As an aside here, statistics tell us that a unit over 3 years old IF repaired this unit, will usually fail again within the next 6 to 12 months anyway, with a differing problem, or a repeat of the same/similar. (This is usually due to the stresses on "Other" .component already slightly damaged.)