While better quality audio cables will help you will be limited by the quality of your video capture card.  I tried converting my home movies myself and then realized the quality was awful and switched to StashSpace.Com a video tape to dvd conversion service.

They convert the tapes for you.  When I did it they were running a promotion where the transer to digital was free and you just paid the $15 for a DVD.  You can use their online software to watch, share, and edit which is nice if you want to combine footage from multiple tapes.

You may want to check them out to see how much better the quality is.  I highly recommend them.  Go to http://www.stashspace.com to check them out or give them a call.  Good Luck!