I'm not a PC expert (Mac guy, sorry!) but it looks like you will eventually need more RAM and perhaps additional hard disk space. 256mb may limit your performance and I think most people use a minimum of 512 and up. Your 40 gig drive will fill up after a few months of recording unless you plan on a limited number of tracks per song or have some type of external storage device. It's also ideal (though not required) to have recording software and song files on separate drives. I can't say much about your Celeron 1.7--again, I don't use PC's so I don't know if this processor is suitable. Hopefully, a PC user will chime in an settle this!
You didn't say (or I didn't ask) if your PC had a free USB port, a firewire (IEEE1394) card/port, or an available PCI slot. You will need one of these to record into the computer. And what you have available will determine which type of soundcard or interface (USB or firewire) you will use. Again, I'm no PC expert, but I assume (for quality reasons) you don't want to use the existing Soundblaster card. Many people use soundcards and if you are comfortable with the installation check out some of the possibilities:
http://www.zzounds.com/a--2676837/cat--PCI-Audio-Interfaces--2421
The key is to find something that meets your needs in terms of INS/OUTS and works with your computer, processor, chipset, etc. If you don't replace the soundcard, the other option is a USB or Firewire interface:
http://www.zzounds.com/a--2676837/cat--USB-Audio-Interfaces--2424
http://www.zzounds.com/a--2676837/cat--Firewire-Audio-Interfaces--2420
Browse through these options and do some research on this board regarding issues with specific interfaces.
Once you tackle this, you will need some recording software. If you are on a tight budget, check out N-Tracks. You may also get free/bundled software if you buy a USB or Firewire interface. Digidesign's Mbox, for example, comes with ProTools LE and MOTU Firewire devices usually include AudioDesk. You can also choose from a wide variety of other options including Cubase, Digital Performer, Logic, etc. There is a long list of possible options and many offer approximately the same quality and options. Take a look around this BBS. Someone is always asking for advice on the "best" software program. The key, IMHO, is to make sure the software is compatible with your interface/soundcard and your system. Many programs can be downloaded as demos, so be sure to test before you buy. After that, I would argue that almost every software option is going to have a steep learning curve. So you need to jump in, read the manuals, and find a good users group where you can ask questions.
After you get this mess sorted out, you will probably want a stand-alone recorder!