If you are using Windows 8 (or later) then try this:
"C:\Program Files (x86)\Common Files\ArcGIS\bin\EsriRegAsm.exe" <Geoprocessing tool DLL> /p:Desktop /s
With regard to messaging/logging, have you tried adjusting the "Message Level" property on your Geoprocessing service? See screenshot below. This property allows you to control the minimum severity level of messages sent to clients when they invoke your Geoprocessing service.
Finally, you may need to register your Geoprocessing tool on the server by using EsriRegAsm.exe, e.g.:"C:\Program Files (x86)\Common Files\ArcGIS\bin\EsriRegAsm.exe" <Geoprocessing tool DLL> /p:Desktop /s
Before getting too spun-up on logging or debugging, you may want to first check that your Geoprocessing tool(s) are valid and runnable on the server itself. When you publish a Geoprocessing tool result as an ArcGIS Server service, a copy of the tool and its support assemblies is uploaded to the "arcgisinput" folder on the server, e.g.:
[INDENT]C:\arcgisserver\directories\argissystem\arcgisinput\<folder name>\<service name>.GPServer\extracted\v101[/INDENT]
I recommend using ArcCatalog to navigate to the Geoprocessing service's "arcgisinput" directory on the server and checking if your tool(s) can be ran directly.