You don't need to part with the content of those CDs and DVDs, just get a few hard drives/SSDs and copy all the media on to them. You can even get software that will compress your DVDs into much smaller video files, and your music into much smaller FLAC or mp3 files. Windows Media Player or VLC will do the CD-MP3 conversion (and to FLAC I think, which is optimum quality), you can download other software to compress and save your DVDs. All you need is a PC or laptop with a DVD drive (and to download DVD compression software from the Internet).
You could even send your discs to a third party to do all of that for you, but they will charge a hefty premium, easy enough to do it yourself IMO (although depending on the size of your collection it could take a few weeks to convert all the media). In my experience, a full CD takes 5-10 minutes, a DVD more like 1/4 hour to 1 hour.
But the beauty is, when you're done you have your whole music and film collection on hard drives, searchable and available within seconds. It's a worthwhile mission IMO. A compressed DVD film should take up no more than 1 GB, a FLAC music album should take up 3-500MB. That means with a couple of 1TB drives you should be able to get at least 1000 movies and 2000 albums. If you have HD films, or want to save the films uncompressed you'd be looking at a bit more storage, but not a lot more.