You could get Audacity. It is a very popular, free GNU-licensed recording and editing program. It has a lot of functions available but does lack some sophisticated ones.
Your PC, just by itself, likely has a stereo mini-plug for a stereo mic. Or you can purchase a stereo to two mono adapter cable. You will be best off with two microphones. I used two Radio Shack (shure rebranded) omni-directional mics for years with my DAT deck with good results. For your practice sessions, you could do with regular mics but will need adapters to 1/8" mini plugs and that is where things can get sticky. XLR adapters to 1/4" or 1/8" usually cut the dB output of the mic and can mess with recording levels. You can purchase lo-Z mics cables with 1/4" phone jacks and do a 1/4" to 1/8" adapter on each, that should work fine. More expensive options include buying cards with microphone XLR connectors, etc. and assigning inputs to the recording programs such as Audacity.
But, with a setup of two mics into the mic jack, you would create two tracks in Audacity, assign one to the left channel and one to the right channel and hit the record button. Since you are recording band practices, you probably don't need to do much else except for adjust the mic volume. N.B. your laptop likely will NOT support the new powered stereo mics from Sony (unless you have a Sony Viao laptop and then I would check the PC manual). Depending on what you want, you could stop and save each song after you have finished and start a fresh recording or (what I do) is record the entire session and edit the songs later with the editing function and save out the individual tracks.
Sorry to hear about your H2 troubles. I have one and I love it. I just set it up in the middle of the jams that I participate in, hit record and let it go. Then I copy to my computer and edit the songs out there. I usually do a save at set breaks. I also use the normalize function on the H2 to bring volumes up, but I know what you mean about the small screen, etc. That is why I don't try to edit or do much else on the H2 itself.
Hope this helps some... good luck!