I am afraid that what you are trying to achieve is not really possible.
The best you could do is set an calculated attribute on your incident (for example IncidentColour). Create a calculation that outputs something based on your conditions. For example if assigned group = a and status = b: value = 'green'.
This should be an easy calculation to make.
Next you can create an html template and put your color in there somewhere. What you can certainly do is have an image or something in a column based on the color.
<tr><td>images/{IncidentColour}.jpg</td><td>Description</td></tr>
If you make sure you have a green.jpg image in an images folder (in my example, this will vary depending on you configuration) this will show you an image based on the calculated field.
In a perfect world you could also do something like this:
<tr bgcolor="{IncidentColour}"><td>Description</td></tr>
Since the css code is inline, it should work, but as you mention in your question, it could be overwritten by the css of the application ...
This answer is just a place to get started, don't hesitate to ask if you have anymore questions on how to achieve this.