You are missing the CSS code for the slider that will style it.
If you have “Enable WooCommerce CSS” checked in the General WooCommerce settings page, it should show up.
If you are doing custom CSS styling, you need to style the slider elements.
Here is a slightly modified version of the WooCommerce default price filter CSS:
/* =Price Filter Widget
-------------------------------------------------------------- */
.widget_price_filter .price_slider {
margin-bottom: 1em;
}
.widget_price_filter .price_slider_amount {
text-align: right;
line-height: 2.4em;
font-size: 0.8751em;
}
.widget_price_filter .price_slider_amount .button {
font-size: 1.15em;
}
.widget_price_filter .price_slider_amount .button {
float: left;
}
.widget_price_filter .ui-slider {
position: relative;
text-align: left;
}
.widget_price_filter .ui-slider .ui-slider-handle {
position: absolute;
z-index: 2;
width: 0.9em;
height: 0.9em;
-webkit-border-radius: 1em;
-moz-border-radius: 1em;
border-radius: 1em;
border: 1px solid #141741;
cursor: pointer;
background: #2d338e;
outline: none;
top: -0.2em;
}
.widget_price_filter .ui-slider .ui-slider-handle:last-child {
margin-left: -0.5em;
}
.widget_price_filter .ui-slider .ui-slider-range {
position: absolute;
z-index: 1;
font-size: .7em;
display: block;
border: 0;
background: #c0132c;
-webkit-border-radius: 1em;
-moz-border-radius: 1em;
border-radius: 1em;
}
.widget_price_filter .price_slider_wrapper .ui-widget-content {
-webkit-border-radius: 1em;
-moz-border-radius: 1em;
border-radius: 1em;
background: #d5d5d5;
}
.widget_price_filter .ui-slider-horizontal {
height: .5em;
}
.widget_price_filter .ui-slider-horizontal .ui-slider-range {
top: 0;
height: 100%;
}
.widget_price_filter .ui-slider-horizontal .ui-slider-range-min {
left: -1px;
}
.widget_price_filter .ui-slider-horizontal .ui-slider-range-max {
right: -1px;
}
That should get you started!