Hi folks, 
 
I've had an ongoing issue with starting my MR2 for as long as I have owned it, I am going to replace the immobiliser (Mongoose) on the weekend, hopefully that will resolve my issues. I am putting this post up in the hope I can get some suggestions for other bits to check while I'm ripping things apart so I can be 100% sure the issue is fixed for good.
 
90% of the time when I disarm my immobiliser and turn the key to ON all the warning lights come on the dash, in the bottom left corner the P/S and ABS lights turn off while the check engine, battery and oil light stay on, I can start the car normally and the rest of the warning lights turn off, nice normal behaviour.
 
The other 10% of the time when I disarm the immobiliser and turn the key to ON only the P/S and ABS lights come on in the bottom left corner and stay on. The check engine, battery and oil light do not come on. When this happens I can crank the engine over as much as I like, the car will not start.
 
I am thinking my issues are being caused by the immobiliser as this also happens if I turn the key to ON with the immobiliser still armed.
 
I also have an issue with the car suddenly cutting out while driving, when this happens the engine just cuts out, the P/S and ABS warning lights come on, with no check engine, battery or oil warning lights. I can not start the car again until these come back on.
 
I have found that quickly flicking the key all the way off then on can sometimes bring the 3 missing lights back and I can start the car, sometimes I can sit there for a few minutes flicking the key and waiting. If I am too vigorous with my key flicking I can see the 3 lights come on, but I flick back to off then on again and they don't come on.
 
I'm pretty convinced the issue is caused by the immobiliser, it doesn't seem to be any worse if I have A/C, stereo, lights etc. turned off / on. It does seem to be worse in the morning when I first start the car. If I have been driving around for a while then turn the car off, I can usually start the car again without issue while it is still warm.
 
Sorry for the lengthy post, thanks in advance for any help and suggestions!
 
Cheers,
 
-Whitchy-

Turns out this was a simple fix, my starting issue was being caused by a sticky relay for the immobiliser. When I had the relay in my hand I could turn the key to ON, if the dash lights didn't all come on I could flick / tap the relay and it would come good.
Replaced with a brand new relay and its been perfect all weekend!
 
Cheers.

Good to here it has all worked out for you.