Those matrix panels require 5V to operate. Providing too much voltage (7.4V) will destroy the LED matrix. You MUST provide the correct voltage for this to operate, it looks like it may be too late from your picture though.
Something like this would work, you need 5V and at least 4A:
You scared me there for a minute! One of these will work, it can handle 6A and your matrix should only draw about 4A. This will give you a little overhead so the regulator won’t get as hot, and you could use it power your Arduino as well so everything could run off the one battery. Actually if you could power the Arduino directly off the 7.4v battery as long as you go through the 2.1mm power port. There is a voltage regulator onboard that can handle up to 12V.
Under power will affect it in one of two ways, if its just under you will probably just get a slight dimming of the lights as the unit struggles to provided the current needed. The other will be the voltage will drop a lot and you will get no lights at all. These cases should not damage your hardware at all though if you have any components with writable memory it may cause corruption.
I’ve managed to get the raspberry to to control the matrix board I’m trying to make it run through a sequence loop but it seems to stop after about 5mins. Could this be the raspberry going to sleep
It could be, but that seems unlikely. The Pi will not go to sleep unless you have configured it to do so. This could be a result of being under powered. Do you get any errors from your Pi program when it stops?