Screen sharing problems

Question

Hi,
I have a strange problem when I try to connect to another Mac in my home network via screen sharing. Here's what happens in case somebody can help me.
I'm trying to do this via Finder. I go to 'Shared' on the left column of finder and place my cursor on the name of the other computer in the network and I click on the 'Share Screen' button. When I do that, a little screen pops up saying "contacting 'other computer'"
And after a while, the following error message appears:
"Connection failed to 'other computer'"
Please make sure that Screen Sharing (in the Sharing section of System Preferences) is enabled on the computer to which you are attempting to connect. Also make sure your network connection is working properly."
However, Screen Sharing IS enabled in System Preferences (on both computers). I disabled the firewalls on both computers as well in case that was the cause of the problem.
I have been wracking my brain trying to troubleshoot this and I've found some strange things that might be connected to the problem.
I think I must have messed up something changing the name of the other computer. This is a computer that I have in another room of the house (from now on 'Computer 2', 'Computer 1' being my computer, the one I'm trying to connect from). In this computer I have various accounts for my children, for myself and for guests. The thing is that before the computer used to have another name (I don't remember the exact name) and then I changed it to Marta.
Since I did that, when I look at the public folders in Computer 2, things are a bit amiss.
The first thing I notice is that now the public folder looks different from the other folders:
http://img146.imageshack.us/i/computer1mountfinder.png/
View of the folder on the desktop:
http://img717.imageshack.us/i/computer1mountdesktop.png/
i.e it doesn't have the three little guys that mounted folders usually have.
The second thing I notice is that now I can drag files to that public folder but I can only see the files that I have put in there at the moment. If I turn off the computer and turn it on again, I cannot see those files any more. Nevertheless, the files are there. I can see them when I go physically to computer 2 and I look at the contents of the public folder.
Furthermore, I noticed that if I click on 'connect as' and I introduce the login name and password for my daughter's account, then I get to see another folder called 'mfm' (her user's name) which I don't see before doing 'connect as':
http://img163.imageshack.us/i/mfm.png/
Now, what you have to understand is that 'mfm' and 'Marta' are the same. That is, 'Marta' is my daughter and the name that I gave the computer. 'Marta's public folder' and 'mfm' are in fact also the SAME folder. If I do 'connect as' and enter mfm plus password, I can see all the files that I dragged to 'Marta's public' folder.
So my hypothesis is that I have done something (probably when I changed the name of the computer to Marta) that has screwed up the network settings and now the computer is not recognized when I try to do 'Screen sharing'.
If I try to do screen sharing from Computer 2 to Computer 1, things work smoothly. I get a pop up window with two options:
. Enter your name and password to share the screen of Josep M. Fontana's iMac (my computer)
- by asking for permission
- as a registered user
Then I give my user name and password and I can do screen sharing with no problems.
As I said, when I try to do this from computer 1 to computer 2, I am not offered any options: a little screen pops up saying 'contacting "Marta"' and it stays there until I get the error message.
I've wasted a lot of time trying to figure out what the problem is. I would REALLY appreciate any help anyone can give me to solve this problem.
Thanks in advance.
Josep M.

Answer 1

Please, don't tell me my problem can be solved Perhaps I was spoiled with these forums since all my other calls for help were answered very promptly and with lots of good advice. Is this really such a hairy problem to solve? Was my description not clear? Please, if I can provide any more information or describe again something you don't understand, I will do it gladly but I need urgently to be able to do screen sharing with this other computer. I just added a new Mac to my network (a MacBook air) and I connect to and from it via screen sharing without any problems. So there is something screwed up in the configuration of this particular iMac which doesn't allow me to connect to it.
Please, please, please. I implore the Mac experts that hang out in these forums to lend me a hand.
Josep M.