I have drawn 2 circles as well as 2 staring lines. I am trying to cut out a chunk of the circle where the lines are. I've tried combining the circles, then using the Division function and it is not working.

Are your lines above the circles? Do they extend beyond the edges of the circles? Are these lines meant to be joined to cut the shape from the circle ? Or is each line cutting off a separate piece?

Is there any message in the taskbar at the bottom of the screen?

What actually happens when you click Division? What do you see?

Can you attach an image of what you are trying to do.

If you want to split lots of shapes into intersection component parts. 

You can select all shapes, Path>combine

then draw a rectangle which covers the combined path, send the rectangle to back. Object>Lower To Bottom

Select all, then choose Path>Division

Attached is a sample of what I'm trying to do. Id like for the blue lines to cut both circles.

Draw a circle with a broad stroke which will represent the outer and inner radius. Then go Path->Stroke to Path and adjust no fill but stroke color - give it now the thickness for the end result. Now draw a rectangle ( fill/no stroke); the bottom will be the horizontal blue line and the right side the vertical blue line. Select both shapes and go Path->Difference.

Wow! That worked! Thank you so much!

Just in case: I´m not sure if you want the shape to have openings at the straight edges - if so you can select the 2 nodes of each (simultaneously) with the Node tool and go "Delete segment between 2 non endpoint nodes".

ANd don´t forget you can draw partially circles with the circle tool - duplicate and scale from the center - just for inspiration.