Do I have to use EXACTLY the same power cable
As long as it's 18V, &gt;= 1.3A and has the same plug polarity, you can use it. You can also cut the jack off and put a new one on (or just push the cord through and re-attach it).
If you do cut the end off, I'd recommend using butt-splices (if you can't solder/shrink tubing) to put it back on, or get an end with screw terminals:

Just pay close attention to the polarity when you reassemble.