The purple vertical lines (in addition to the other fault) make me think more of a graphics chip problem, or even a cable problem between the base and display. Note what it says about overheating problems with graphics cards in this model - adds weight to the faulty card suspicion.
The Inspiron 8500 actually has a replaceable graphics card, so it's possible that a new card may fix the problem - don't know where you would get a card yet - but it must be possible. Guide to doing it click here Other tips on better graphics card card cooling for this machine on the same site.
Don't ask me how you can prove whether it is the display or the graphics card - because that'll be very difficult if you don't have another graphics card to try in it.