If I take my Dell Dimension Desktop to a point that is outside the range of my exisiting home wireless network, is there a way I can extend that range?

 

Yes, you could add high gain antennae or cantennae to increase the sensitive to the signal.  You could also add a dedicated wireless signal booster/repeater half way to boost the signal, although user reviews as to their effectiveness have been mixed.  Some Access Points can also work as a wireless repeater with the appropriate router, e.g., Linksys WRT54G+WAP54G

 

If I attach another Router to the computer that is out of range, will that new router send out and receive the signal from the router that is currently in use on the network? Would that extend the range and thus give me access to that existing network?

 

Not usually, but it also depends on the router model.  For example, Buffalo routers have WDS (wireless distribution system) for this purpose so you wouldn't need a wireless repeater.  A 2nd Linksys WRT54G can also act as a repeater by cable connection to another WRT54G.  WRT54G can also have WDS by use of custom firmware, but this has become incompatible since WRT54G V5.

 

Does a router act as a receiver as well as a transmitter?

 

Yes, it does.  Data travels both ways on a wireless network, just like on a wired network - from your wireless computer to the router and vice versa.

 

Could I extend the range as well as make my Dimension wireless capable by adding that new router?

No, since your original signal is out of reach.

 

If you have a DELL router, please do not use any other extender, other than a DELL. DELL does not manufacture extenders, but you could buy another router and bridge the routers and create an extended network.