to broadcast a network from your wireless card you need to set the card to create a adhoc network, a point to point network wireless with other pc
if you haven't done this, you are not broadcasting any network
a card without the antenna, has as little coverage as 1 meter of distance, if your router is at 2 meters, you could not see it or get just 1 or 2 bars, sometimes with wpa2 tkip this won't be enough to establish connection, sometimes could be enough with wep
normal neighbors will not see you, they might see you if they assemble a very big directional antenna, something like a yagi uda antenna designed to work in the specific frequency you could be broadcasting, connected to the router but still, you need to create the adhoc network
if you lost your wifi card antenna, a old trick that sometimes works is connect one of these

to the internal conductor in the exterior of the card

only the internal part should make connection, not the internal conductor and the external, this will give you a decent connection, 4 to 5 bars, we do this on class all the days because some guys decided to steal a bunch of antennas so we had to find a option and this one was simply enough, monday will bring a picture showing how we do it