Have an interesting question, in fact it seems to me to be quite the newbie question.

I have a wireless D-Link router connected via RJ-45 (wired connection) to a another D-Link router (NOT wireless), which in turn is connected to my DSL router. After numerous problems on getting wireless to actually connect, and MUCH time with tech support, they had me change the wireless router into a "pass-through" router only.

OK, here is the question... based on the above setup, I've set all the computers within both the wired and wireless networks with individual IP addresses, and have enabled sharing rights very stringently within all computers on the network. My DSL connection requires a specific IP address, gateway and DSN address for ANY connection to actually connect to the internet. Because of this, I have deliberatly refrained from turning on the WEP or any other router encryption or security for speed purposes, and to be honest... because I don't want any more problems with my wireless connection. I've based this decision on the fact that other family members have tried to get onto the network when they come to my home with their laptops, and unless they know the gateway and DNS addresses they are unable to connect to the internet... they are able to see the network and its wireless connection, but cannot access it.

I fully realize that this is not considered a secure connection by any means, but with this setup, can anyone tell me why I would still need to enable WEP or WPA when without the necessary IP addresses a person is unable to access my network?

Another issue/question is that if and when I ever turn on WEP or WPA how will/can that effect my wireless connection via a "pass-through" router, since I'm very nervous to actually "try" it to see if it will work?

Simple. Have you ever tried running ipconfig on the command line? It gives out (at least) the gateway's IP address. Sure, DNS may still be a problem, but that can also be fixed if the hacker knows the specific IP address of another DNS server.
Good point. Encryption can lead to all kinds of problems, from packet dropping to no connection whatsoever. My suggestion: turn it on, and see how it works. If it doesn't work well, you can switch it off, because it will be highly unlikely that you can wreck anything simply by turning encryption on/off.