Press Home then Shift+End.
End then Shift+Home can also be used. If you need to select the line from the very beginning instead of the first indented character, press Home twice.
You can also record this as a macro and then set a shortcut to that macro. However Ctrl+A is used as select all in almost all text editors and textboxes, thus changing it could make things more confusing. Use another shortcut instead
If you just want to copy/cut/delete the lines, there are already shortcuts for you:
- Line delete Ctrl+Shift+L
- Line cut Ctrl+L
- Line copy Ctrl+Shift+T (changed to Ctrl+Shift+X in newer Notepad++)
There are also other actions without default shortcuts like line transpose, line join, line duplicate... Just select Settings > Shortcut mapper > Scintilla commands, select
SCI_LINESJOIN... and assign them.
If Ctrl+Shift+T doesn't work for you then it's because the shortcut has been assigned to 2 different features, causing a conflict as PryrtCJ answered below. In newer Notepad++ line copy has been changed to Ctrl+Shift+X, and a shortcut conflict warning has also been added, making life a bit easier
See Lists of default mouse and keyboard shortcuts for Notepad++ and some plugins
If you're using a mouse, single click the line number on the left or triple click in the line also do the trick.