Actually, you want them in series, like a flashlight.  Then you add the voltage
 - battery +  - battery +
You supply the laptop from the far left and far right ends.  Suppose you use 2 x12 v 5 amp hr. batteries - this will yield 24 volts @ 5 amp hr
If you connect them in parallel, you'd get 12v @ 10 amp hr.
It wouldn't surprise me if the connector is tough to get - even from Dell.  You could always cut your existing wire and put your own connectors on either end of the cut and put a matching connector on your battery.  That would allow you to use the same part for either your AC or your battery supply.
I just measured the supply from my Dell 1100 and it was 20 v - exactly as marked.  So if it says 19, it probably is.  I'd recommend two 9.6 v packs and you won't have any worries.  Unless you really wanted to haul lead around  

  I'm really not sure if 24 is OK -  you might want to check that elsewhere before something blows up.  Safer to put a regulator between the battery and pc (easy but still more ambitious - the high current draw will probably generate a lot of heat).  Keep in mind that your built in battery back is probably 14.4v so you'd be safer with 3 x 6v or 2 x 9.6 v
Also, that thing near the end of the cord is a noise suppressor - you sometimes see them on modem cables as well.  I wouldn't worry about it.