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.