Yes the timing is as it should be as per the manuals, this is why I am wondering if the CDi unit is the problem anyone know what issues a faulty one can create? As I said the plugs are sparking when the engine is turned over on the start button.

 

Weak , intermittent or no spark at all relative to the spark box.

So tell me have you attempted to jump/boost it with cables from a car ???

These damned bikes need 110% battery to get going when cold or not started
for a long time .......had this issue with my 90 the other day and it has a
100% good battery ........but it took a boost to get her "to fire" ...but then it
was 12F out in the garage at the time too

 

Is is possible with the amount of carbon you saw on the piston crowns that some has actually gotten under the valves and is preventing the intake valves from closing completely?

That would offer some explaination to the fuel being blown out the back of the carbs.

Otherwise I would look toward SPROCK's suggestion: check both the ignition timing and the valve timing.

Be carefull that you don't get a "backfire" when the fuel coming out the back of the carbs gets ignited! Flame on!

 

For fuel to be blown out the carbs, I would check the intake cam. When a cam is off it will try to start just like you have described.

 

I would say plugs leads on wrong. I had a vf750f, compression fine, fuel going in, timing bang on and fuel spitting back. I got the bike and assumed the PO had put the leads on right, he couldn't get it to run.

Got access to another bike checked the leads mine were wrong put them on right and after blowtorching the plugs to get them clean it fired up first prod of the button.

When on the saddle of the CBR left coil should go to cylinders 1 and 4 and the right hand coil feeds 2 and 3.

 

These were my original thoughts. If someone else has been fiddling about you don't know what they've done or if they've done it properly

Start with the basics and work through, I doubt the PO would have got to the point of changing the timing