Go talk to McClure, and tell him you've solved the problem. He'll make you a citizen. I also asked him for permission to use the reactor disc on their computer. I'm not sure it was actually necessary, but what the hey... (If you ask him about the optimization before telling him you repaired it, and becoming a citizen, he'll run do it for you.)
Now go into the actual vault. If you have good medical skill, search
their medical database computer, on the first floor. You'll find the
details of combat implants. Keep searching for a while, and you'll
get 500xp. You can also discuss medicine with their doctor.
Talk to the nurse. Ask about the city, then work your way to how
there aren't any children, and how come people don't just get pregnant
from having sex. There's 300xp in it if you convince her they may
well be all sterile from radiation. Another 300xp if you can convince
her to go see the outside world if she's that bored inside. If you
have a male character, you can also date the nurse for 100xp. And you
can do the whole sterility conversation again, up to the point where
you get the choice to "donate". That's worth 500xp.
The doctor will also ask you for some Jet for his research. Since now
you're a citizen, you're no longer searched at the gate, so you can do
this whenever you have some Jet to spare. (Can be found on some
Go into the vault and search though all the lockers and footlockers,
on floors 2 and 3. Most of them are hidden by walls and locked, so
a decent lockpick skill comes in very handy. (The stacked crates just
contain tons of water chips which arrived here instead of Vault 13 :)
On the second floor, the rattling vent contains a bunch of
micro-fusion cells. A hidden footlocker contains a computer voice
module, which you'll need later to fix the vault 13 computer. Take
it, and keep it for now.
On the 3'rd floor, make sure you have the reactor data disc in your
ready item slot, before clicking on the central computer. It's the
talking computer. You can also use the science skill on a terminal
near the south-west corner of the level for 300 xp.
After you get the computer to optimize the Gecko reactor data, leave
the vault. Outside, stop to talk to the geezer preaching in an
intersection, pretend to be interested, and get a suitcase for the
Bishop family in New Reno. Leave the city and head for Gecko.