That was critical information. If the Windows shortcut properties program says it's not valid, that means RomeTW.exe is not there, or the folder isn't. As you have spaces in your folder name, that's probably the problem. Try hyphens around both the Target exe (excluding the switches I think) and Start in:
"D:\Games\Rome - Total War\RomeTW.exe -mod:eb -nm -show_err"
"D:\Games\Rome - Total War"
If it does not help, please do post a screenshot or I can't help you any further.
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