Why try to reinvent the wheel? There are more lightweight jQuery slideshow solutions out there then you could poke a stick at, and someone has already done the hard work for you and thought about issues that you might run into (cross-browser compatability etc).
jQuery Cycle is one of my favourite light weight libraries.
What you want to achieve could be done in just
jQuery("#slideshow").cycle({
timeout:0, // no autoplay
fx: 'fade', //fade effect, although there are heaps
next: '#next',
prev: '#prev'
});