The only software you can use is Backup MyPC to restore from your qic files. I am not sure about V7, as that only came out with EMC9. I have not been able to find a standalone version. That one with updates was supposed to be able to run under Vista, but I have no experience with that. The only thing I can suggest is to find someone who runs Vista, install BUMP to their machine, restore to a external drive, and then hook that external to your new machine and copy file. Something like that is the only way you are going to get that to your new machine.
As for browsing, there is no way as that of it's proprietary compression. They only way to find what is on there is with BUMP. There may be something else, but you will probably have to do a search on the internet for that. I have never heard of one though.
I have kept looking for a new version from Sonic/Roxio but have about given up hope. For the new machine, I assume BackOnTrack will work. Acronis 11, Genie Soft backup will also work as will many of the ZIP programs like PowerArchiver and WinZip.
Sorry I could not be of more help, but there are many products that still have not come out with versions for Vista. One of the many reasons I am staying away from it for as long as possible.