Tomcat is not running even though JAVA_HOME path is correct

Try installing java somewhere else - in a directory without spaces. Set again the JAVA_HOME variable and try again. I remember Tomcat had some problems on Window XP with spaces if any variables it was using while starting contained spaces. Maybe it's similar with Windows 7.

I remember I had to change some lines in Tomcat java classes which were handling Tomcat startup.

@Edit: Luciano beat me to noticing it but you should also remove bin from JAVA_HOME

@Edit: I also remember that another fix (didn't test it myself, though) was to set JAVA_HOME to the shorthand version e.g. C:\Progra~1\Java\jdk1.6.0_25

I think that your JAVA_HOME should point to

C:\Program Files\Java\jdk1.6.0_25

instead of

C:\Program Files\Java\jdk1.6.0_25\bin

That is, without the bin folder.

UPDATE

That new error appears to me if I set the JAVA_HOME with the quotes, like you did. Are you using quotation marks? If so, remove them.

Avoid semicolon in the end of any environment variables... from JAVA_HOME or JRE_HOME

JAVA_HOME=C:\Program Files\Java\jdk1.6.0_25\bin

and

JRE_HOME=C:\Program Files\Java\jdk1.6.0_32\jre

should be like as shown...