does this have any effect on the other devices which will still have it in their settings?
Yes, you would need to set the wireless configuration for each wifi device to open, and set it back again after testing, including re-entering the pre-shared key (PSK). I find that copying the key into a text file and storing it on each computer that requires it saves a lot of typing!
However, we're still in 'problem discovery' mode, so if you can live with changing the "wireless settings\security options" on the DG834Gv3 to "disable" for 5 minutes whilst then trying to connect with the N110, you can see whether it'll get an IP address and then can re-set all your security settings back to what they were after that period.
(although I would reiterate what the grand poobah of PPRuNe has said about your use of WEP. You will have at least the option of WPA-PSK on the DG834G, and you should use it.....if the rest of the devices you wish to be wireless can connect, of course!)
Therefore, the summary being, if you can connect properly with no wifi security enabled on both the DG834G and the N110, it's going to be a driver issue with the Atheros chipset in your laptop.
I would urge you, if successful, to try enabling WPA-PSK on the DG834G with a passphrase of at least 8 characters and connecting via the N110. This would then show you that you could migrate the rest of your wifi-enabled devices on your LAN to WPA-PSK.
(a little note - I've come across this issue twice in the last year, and both times it was fixable by upgrading the NIC drivers or firmware. Neither was on an N110 though, but both were Atheros against a DG834Gv3).