Try verbose upload (hold shift when clicking the upload button). The main thing it will tell us is if there's no communication happening at all with the board, or incorrect communication happening. If there's none at all, it's hard to isolate the problem. Try pressing reset a bit sooner; the bootloader on the Mini should wait 6-8 seconds or so before giving up and starting whatever sketch is already on the chip.
Did you connect the grounds between the Mini and the USB-serial convertor?