1. It sounds like you know about both of the Volume Controls. But it might make it easier on you if you keep one of them at max and never change it. Maybe max out MC's volume at 100%. Or system at 100%. If you have an external volume control (on an amp or receiver for example), you might just max out both. I don't think this is your problem; I'm just addressing it to be sure.
2. It's normal for some songs to be very quiet and some to be very loud. An average stereo system should be able to play either at a somewhat normal volume. I'm not sure how much of a difference you're hearing. Really quiet classical, compared to full volume Pop, Rock, Metal will DEFINITELY be a big difference.
3. Your old player might have used volume leveling. It might have used dynamic range compression. It's hard to say. You can definitely enable Volume Leveling in MC. But, for best results, MC needs to analyze the volume of each song. Here's what I would do as a test:
Find 3 to 10 songs that you like that seem to play at different volume levels. Analyze them in MC: <right click on songs> Library Tools > Analyze Audio > (run it)
It should only take a few seconds per song to analyze. Once that's done, set up the DSP Studio to do Volume Leveling: Player > DSP Studio > Volume Leveling > (check the box next to it)
You may find that this reduces the overall volume; this is normal. To bring some of it back, turn on Adaptive Volume:
Player > DSP Studio > Adaptive Volume (check the box) > (Select Peak Level Normalize)
If that works (and it should), you'll want to do Analyze Audio on all of your files. It might take a while with a large library. You can leave it running while you do other things.
Good luck!
Brian.