To address a few points:
There are two separate issues here - RIPPING (copying, whatever), and BURNING.
With a laptop, the best you can do with the default hardware is BURN games.
To RIP them, you'll need one of the above mentioned tools. In your case, I'd recommend an external Kreon drive.
To BURN them, you'll have to have a compatible burner. Please note, you do NOT have to bitset to DVD-ROM when you burn games. My backups have been burned using my laptop (Dell Inspiron 1525 with a TSSTcorp DVD+-RW TS-L632H ATA Device), and I haven't once burned a game using bitsetting. Every game is stealthed perfectly and runs beautifully.
Also, you'll need the right media. You mentioned the biggest disk you had was a "LOTR ROTK" disc - that's a copy of Lord of the Rings: Return of the King. It's not a burnable disc. You'll need DVD+R DL (DVD +R dual layer) media, preferably Verbatim DVD+R DL discs. They're somewhat expensive, but you can find decent deals on them from time to time.
Once you've got the right equipment - a device to RIP the games, a device to BURN the games (there are lists online you can check for compatibility, or just ask around), and media to burn the games to, you can move on to the next step: software.
Different members here will tell you different things (though there is an "approved" set), but I would recommend IMGburn as a burning tool. All you have to do is set the layerbreak (tutorials are available), and burning runs smoothly.
Would hammer a bit more out, but I'm a touch tired right now.