No extrusion, but manual extrusion works
I think that you have the incorrect diameter specified (e.g. 2.85 mm instead of 1.75 mm) in your slicer; this also appears from a calculation, see below. Note that you can calculate from extruded volume entering the hotend, or deposited volume. For the first you could calculate the line width of the deposited line and verify that with the settings; from the second you can verify if the volume for the extruded filament equals filament volume based on extruded filament going into the hotend for an assumed line width. Do note that (certainly for first layers!) modifiers may be in place. This is merely to get a ballpark feeling for the chosen filament diameter.

If you look at the first move from:

G0 F3600 X-7.753 Y4.378 Z0.3


to:

G1 F1800 X-8.127 Y3.918 E0.01115


You can calculate the travelled distance $ s = \sqrt{{\Delta X}^2+{\Delta Y}^2} = 0.59\ mm$. Also, from these moves you can see that $0.01115\ mm$ of filament enters the extruder $(E)$.

The deposited volume ($V_{extruded_filament}$) of the printed line  equals the cross sectional area $\times$ length of the deposited filament path. Area could be defined as taken from e.g. the Slic3r reference manual to be: 



Basically (as we apply conservation of mass) the filament volume $(V_{filament})$ entering the hotend need to be the same as the extruded filament volume $(V_{extruded_filament})$ leaving the nozzle; so $ A_{filament}\times E = A_{extruded\ filament}\times s $.

This latter equation can be solved for $w$ by filling out the known parameters. From this calculation follows that for $1.75\ mm$ filament you get a calculated line width of about $0.22\ mm$, and respectively for $2.85\ mm$ filament you get $0.46\ mm$ line widths.

As the nozzle diameter has not been specified in the question, but most commonly used nozzle diameter often is $0.4\ mm$, and modifiers for the first layer are at play to print thicker lines; you most probably have the have the wrong filament diameter set if you have a $1.75\ mm$ extruder setup. Basically it under-extrudes.