Compatibility issues between your PC’s wireless adapter (not router) and your DIR-615 wireless router are highly unlikely. All that matters is the wireless adapter and wireless router support the same protocol(s), i.e., B, G, or N (which they do) and wireless security capabilities (i.e., WPA/WPA2), again, highly likely they do.
If possible, use a wired connection initially just to make sure it's not a general problem of connectivity between the PC and the router (vs. being wireless specific). Next, briefly disable wireless security on the router and see if the PC now connects. If it does, then there's an issue w/ your wireless security settings.
If all else fails, do a factory reset on the wireless router (while powered ON, hold the reset button for 30 secs and release) and start fresh. Wireless security will be disabled as a result, so it might be a good time to try the connection w/o wireless security.
P.S. It’s always a good idea to make sure your wireless router is running the latest firmware (visit D-Link website for updates), and using the latest drivers for PC’s wireless adapter. I have seen issues w/ the default drivers installed by Win7 from time to time.