I don't know about that specific model dazzle, but so many people have had audio issues with the dvc100 (iirc) because the drivers suck.
Personally, I bought a cheaper capture device and an amplified splitter for less than the price of a dazzle.
Regardless of what device you buy, you'll definitely need to split the signal, unless your tv has composite out.
The reviews seem more positive and people can get it to work easier. Looks like it's a repackages EasyCap with some firmware changes.
There's also this:
http://www.amazon.com/Diamond-Camcorders-supporting-composite-connection/dp/B000VM60I8/ref=pd_cp_e_2
Which has significantly more positive reviews and supports 720x480 resolution. I'd probably read up a bit more on that and purchase it if it's good for what you need. The price is higher but the video quality will look better.
I looked up some Diamond VC500 quality tests on YouTube and they seem much better than EasyCap recordings, and most of the videos weren't even rendered properly (black bars, resampling enabled). So yeah, I'd go with the Diamond VC500 for sure.
Have you tried posting on the lost media wiki forums? I'm sure someone there would be willing to take them and convert them just for the off chance there might be something on them that someone is looking for. You'll be surprised, some people are looking for commercials and stuff.
Alternatively, I found this on Amazon for like, $35.
Just so you're aware - the elgato video capture will only do 480i capture and doesn't support 240p which you'll need for NES/SNES. I know this because I have one. If you're looking cheap go diamond one touch capture http://www.amazon.com/Diamond-Camcorders-supporting-composite-connection/dp/B000VM60I8/ref=sr_1_1?ie=UTF8&qid=1424201037&sr=8-1&keywords=diamond+one+touch+capture
If you want something better (which I would recommend) might as well get a dazzle http://www.amazon.com/Pinnacle-Systems-Dazzle-Recorder-VERSION/dp/B0039Y2YDK/ref=sr_1_2?ie=UTF8&qid=1424201078&sr=8-2&keywords=dazzle+dvc+100+capture+card
I'm not familiar with Vidbox, but I use this capture device with VirtualDub: https://www.amazon.com/Diamond-VC500-digital-converter-Software/dp/B000VM60I8/
Here's some more information about the capture process: https://www.reddit.com/r/DataHoarder/comments/j4rwk1/the_how_do_i_digitizetransfercapture_video_tapes/