Obtain the latest non-beta Arduino software IDE / toolset from the Arduino website.
Note they don't say anything about using some IDE version that's been obsolete for years, they say use the latest version of the Arduino IDE.
So we know that one part of that wiki you're using is bad information, this means there's probably other bad information also so try following all the instructions from the wiki I provided a link to instead. There are thousands of people using Marlin with the latest IDE version, I'm sure you can get it working for you too.
Which is the same hardware I used for my laser cutter.
I don't remember having to configure Marlin to work with that hardware previously. Has there been a change to Marlin recently that now requires a different configuration?
By using Marlin-RC rather than 1.0.2-1 I've managed to get the LCD working.
I'm now having problems with defining the Board type as I don't have a heated bed I want to select BOARD_RAMPS_14_EFF but then I get the error below when compiling:
Arduino: 1.6.11 (Windows 10), Board: "Arduino/Genuino Mega or Mega 2560, ATmega2560 (Mega 2560)"
sketch\temperature.cpp: In static member function 'static void Temperature::manage_heater()':
temperature.cpp:800: error: 'WRITE_HEATER_BED' was not declared in this scope
WRITE_HEATER_BED(LOW);
^
exit status 1
'WRITE_HEATER_BED' was not declared in this scope
This report would have more information with
"Show verbose output during compilation"
option enabled in File -> Preferences.
If I leave the motherboard as BOARD_RAMPS_14_EFB it will compile and upload but I get an error on the LCD saying:
Err: MINTEMP BED
I guess I need to comment out part of the configuration.h file which relates to the heated bed but I can't find any instructions on which bit(s) to change.
That's not a download, that's a repository that contains many different downloads. I need the exact download link you used to make sure I'm not wasting my time looking at a different version from what you have.
Apologies - I'm not sure how link to the download. From that page I just clicked on the green 'clone or download' button towards the top right of the page, then 'Download ZIP'.
That configures Marlin for there being no temperature sensor in the bed and it now compiles for me. Note that I don't have any experience with 3D printers and only a minimal familiarity with Marlin and I haven't looked at any other parts of your configuration so you definitely want to be sure everything is set correctly for your hardware.