When I double click on maptools launcher I would get the screen that allows you to set min and max memory, but when I clicked okay it would give me an error and failure to connect to java.
First, make sure when you install Java you use the Windows offline 64bit install found here: http://java.com/en/download/manual.jsp
So, you're getting a "java.ConnectException"?
Are you using any additional firewall or anti-virus programs?
Something is blocking the launcher's access to Java. When you first ran the launcher did you accept the java security exception it asked for?
You can try the developer version that Wolph is suggesting, it has it's own java install... but it has not been heavily tested (i.e. it's a developer version).
You can also try this (note: this assumes you are using version maptool version 184.108.40.206):
1) Open Notepad (Click the windows Start button and just start typing "Notepad").
2) Paste the following text into it (not the word "Code:", just what's in the box below that):
start "MapTool" %JAVA% -Xmx%MAXMEM% -Xss%STACK% -jar maptool-%VERS%.jar run
3) File>Save As
4) Navigate to your Maptool Folder (left panel). Then set the File name as: runmaptool.bat
5) Save. Close Notepad
6) Open your Maptool folder and look for the "runmaptool" file you just created. Double click on it.
7) Accept any security exception it asks for.