Right finally this to work. Firstly, I am putting down everything here I tried that didn't work as it might also be of use to someone. If you have the same problem as I described here, you should do everything here.
In Control Panel \ Network and Internet \ Network Connections \ My Connection \ Properies:
- I ensured Link-Layer Topology Discovery Mapper I/O Driver was enabled
- I ensured Link-Layer Topology Discovery Responder was enabed Tried with
- I tried with IPV6 enabled / disabled
In Control Panel \ All Control Panel Items \ Network and Sharing Center \ Advanced sharing settings and I checked relevant settings in "Home or Work profile".
- I ensured: "Turn on network discovery" is set
- I tried both security settings in "File sharing connections"
In Control Panel \ All Control Panel Items \ Network and Sharing Center
- I wnsure my network was marked as a "Work" network. Ensure this is correct for you.
Ok so none of the above yielded any luck.
Then, I did the following:
At, Control Panel \ All Control Panel Items \ System
I selected: "Computer Name" tab.
- I entered something in the computer description text box. This was blank.
- I selected the Change... button.This gives you the opportunity to change the Workgroup name Mine was "WORKGROUP". I set it to something else and then set it back to WORKGROUP. The thinking was this might flush something.
I then logged onto the machine that had the folder I wanted to share thru RCP. Then I accessed a share folder on my PC. Now, when this session was alive, I opened up Computer Management and I opened the "shared folders" and sessions and saw the computer I was trying to connected, connecting to me.
Again the thinking was this would flush something out. After, I did all this it worked. I am not sure exactly what step fixed it. I was under too much time pressure to keep checkeding after I changed anything.
Thanks for all who helped out here.