Need help with my audio setup for my computer

The problem is, I think, that with the old 2.1 speaker system the amplifier for all 3 speakers was in the subwoofer, and that is now gone.
I'm not sure why you have coupled together two 3.5 mm connections from your PC, but we can get to that. In any case, the outputs from your PC are called "Line Outs" in that they are unamplified, and low level. Connecting that to the new sub's "Line In" should work fine, but the problem is the sub isn't really meant to power/amplify other speakers, and certainly not via the "Line Outs" because as we know now, that is low level/unamplified.
You can try connecting the 2 satellite speakers to the "Hi Level Out" speaker connections and see if they work that way. To be honest, I've never tried that, and it's possible the sub has to have Hi Level Inputs connected (which you can't do) in order to pass Hi Level sound on the outputs. You can try, but alternatively you need a Surround Receiver/Home stereo system that supports powering two speakers and has a line out for the sub. You could easily get a used AV Receiver locally for cheap.