PL2303HX programmer not responding

Unfortunately, your image on "imgur" appears to be highly toxic to my browser or picture viewer (crashes Xwin), so I cannot see what sort of PL2303 module you are using.

You say it works fine with the FTDI chip. It should then be quite possible to manually upload or indeed to use the PL2303 chip. Does it not have DTR brought out to a "thru" on the board already? I suppose the five pin variants do not, by and large.

As to the timing, you do not need to hold the reset down for a long time. Just briefly press it when you see the "Binary sketch size: xxxx bytes (of a 30720 byte maximum)" message.

And - just in case, - try not crossing over TXD and RXD!