you'd know it if the lcd was broken because ink would bleed all over the screen and you wouldn't be able to see anything. it sounds like you've only broken the glass....which is nice because the LCD is the more expensive part to have to replace.
the LCD and glass are NOT fused as one piece. they fused the glass and the digitizer (what makes your touch screen able to function via touch) as one piece, but not the LCD and glass. it's actually kind of nice that they did this because the digitizer was kind of a pain in the ass to swap from broken glass to the new one. this will dramatically reduce the potential of breaking the digitizer when replacing the glass.
here is a link to the replacement glass and digitizer for an iphone 4g on amazon & it's under $20. without having seen the phone, and based solely on what you've described in this thread, I'm 99.9% sure that this is the only thing that you need to buy. once you have this piece, it's just a matter of popping your old glass/digitizer out of your phone and replacing it with this new one. shouldn't take longer than an hour to do.....tops.