Depends on the model you bought, as I don't believe all of them have wireless built in. I know the early, and now discontinued, 20GB models didn't have it... The newer 40GB model may well lack wireless like it lacks any sort of back compatibility with previous PlayStation console games.
But have you tried a Google search for things like "Playstation 3 enable wireless"? Is your router using any kind of encryption on the wireless signal, and did you configure the PS3 to use this same encryption?
I also must confess I don't know what BD Live is, but if it's any kind of streaming media, your router isn't going to likely be up to the task of streaming that. 802.11g simply lacks the necessary bandwidth. I also hope for your sake that Dlink has solved the manufacturing problems they had with earlier models of that router. Otherwise, do much more than simple web browsing with it, and you will likely cause the thing to overheat and reboot.
I just purchased a PS3 and I don't know how to go online without connecting it using an ethernet connection. I thought this machine was supposed to be able to go online wireless. I only bought it because cnet recommends this as the best blu-ray player available. Just want to watch movies and take advantage of BD Live available from some Blu-ray movies. I do have a router (D-link DI-624) and it works fine with the computers and Wii in the house, but not the PS3 or PSP. Any help would be appreciated.