Okay, with Win 7, you have to do like I had to for Vista.
You can't put SH4 into ProgramFiles x86. It screws the pooch.
Uninstall SH4, and delete your SH4 folder from the Documents folder.
On your C Drive, create a folder called Games or whatever you wish.
Re-install SH4, navigating to that folder. Once you've that, reload JSGME into SH4 and all should be well.
You should be able to remove JSGME with Control Panel. I don't know what they call it Win 7, but for me it is Programs and Features. In XP I think it was just Installed Programs. So simple, but engineers, ................ grumble grumble, ...................... they love to change things..................
Just as a note, I have it installed on my second hard drive in a folder I called Games. I put them all in that folder, so I don't have to go searching high and low for a game I want to mod for myself.