You *can* but maybe don't want to (and won't get a very in-your-face sound) by spending only about $5 on a cable. Put the SM58 on a desk/chair/stand (if you have one), point it at the band, plug it into the mixer, and find/buy a cable that you can take from the headphone output (or perhaps the L-R output, depends what's available on that Yammie) and take it to the blue Line In on any PC/laptop you have kicking around.
Apologies if you've already tried this method.

With the vocalist(s) standing in front you'll get something that's probably "passable" and very easily done. It might sound muffled and distant. It'll probably sound better than a camera's recording from a concert, but not as good as a studio recording.
But to me a demo should show off the music, not the ability to hide under a blanket of mics. Sometimes close micing everything only gives you bad and loud. Depends on the gear and how well you can set it up...

Adding more mics will let you individually mic things and to get an in-your-face sound so the vocals cut, the drums have punch and the guitars sound ... crunchy. Or whatever.

Your other option that someone might mention is to spend part of that $500 on studio time. Leverage their equipment/experience and get something decent down. Buying your own equipment is more of a long term thing - if you want to keep recording demos for the foreseeable future.

Into home recording would suggest a more long term goal. If you want a full setup you're probably looking at 5 mics, one for each instrument. But a lot of times you want more than one for the drummer. The cheaper bet is to use what you have, or rent some studio time, and/or maybe pickup a field recorder like a H1, H2, H4n, PMD661, and progressively more costly options. Or just get a decent stereo pair to use with your current gear. Lots of options depending on your goal(s). Just a demo, or something more commercial. Short term, or long term? Pro like, or best you can get for $500?

It all adds up quickly given that you need a lot of extras beyond just a mic and a mixer. Cables, stands, mounts, ..... When I bought my first decent soundcard (used for $100) I went out and bought $200 in cables, stands, and adapters just to use it. Throw on a mic preamp and headphone preamp, and other things. $500 wasn't much. Your mixer fills in a significant gap there, but hardly even half of the big picture when it comes to pressing record. A feature that your mixer probably lacks. If you don't need to fill a 4' cube of space for gear in your bedroom, or collapse your walls in 6" x4 in treatment. Perhaps rental / studio time is the better option.

500$ is tight.

if it were me, i would get another 57 and a matched pair of condensers. then get the best interface you can with whats left. you will still be doing some overdubs most likely, but it will be workable.

Hey man I saw this article recently and really helped me to wrap my head around everything. Check it out... might help you with your decision making - [[url=http://[/URL]="http://www.waves.co…"]Home Recording 101[/]="http://www.waves.co…"]Home Recording 101[/]

If you don't wanna invest in lots of mics... overdub everything! It depends how much of a "live" sound you want on your recordings, but with that money... Just get another mic for a stereo pair and get crackin!