Short circuit protection problem

I am using a clone Arduino Mega to power a breadboard contraption, but when I attach it to the power rails on the breadboard, the short-circuit protection triggers and the Arduino Mega shuts off. The resistance between the +5V and GND rails is about 1.8 Megaohm, so I fail to see why the short circuit triggers. Does anyone have any idea why this happens?

Post a photo of where you are making connections

It looks messy, but afaik there are no miswires. The circuit has a 65C02 cpu, an Atmel 28C256 EEPROM, a miscellanous quad NAND gate, a 62256 SRAM chip and a 65C22 VIA. Now that I think about it it might be the overcurrent protection, as these are a lot of components. Is that possible too?

I would say it is quite likely you are taking too much power from the Arduino .
The 5v pin is not intended to supply any appreciable load and is not suitable for this task .

An Arduino is NOT a power supply and only has a finite current available.
Agree with Hammy in that you are expecting waaay too much from the Arduino.

A seperate PSU capable of giving you the required current plus a safety margin of at least 10% is what you require.