It's a combination; starter is going and needs a certain minimum amount of current to operate the starterrelay. Your battery is probably not capable anymore to supply that amount of current. Put in a new battery and you'll be good for some time, but you can expect the problem to show up later on.
If the 7m starter works I wouldn't know, I do think a 2jz starter fits.
If the 7m starter works I wouldn't know, I do think a 2jz starter fits.