Unable to upload sketches or bootloader to 5V/16MHz Pro Mini

I recently bricked my 5V/16MHz Arduino Pro Mini. I don't have an FTDI breakout, instead, I've been programming it by removing the Atmega328P-PU from my Uno and the following connections:

Uno-------->Pro Mini
5V---------->VCC
GND------->GND
RX0-------->RXI
TX1-------->TXO
RESET----->GRN

However, after some incident (I'm not sure what happened), I've been receiving the following avrdude errors:

avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x40

(It repeats for 10 tries.) Some tutorials say to connect the Uno RESET directly to the Pro Mini RST instead of GRN (a.k.a DTR) but that produces the same error.

I tried re-burning the bootloader onto the Pro Mini using these instructions, but now I receive the following avrdude errors:

avrdude: Device signature = 0x000000
avrdude: Yikes!  Invalid device signature.
         Double check connections and try again, or use -F to override
         this check.

What should I try next? I have a SparkFun Redboard with a functional Atmega328. Would that be a plug-and-play (or solder-and-play) replacement for the Atmega328 on my Pro Mini (it is a 5V/16MHz Pro Mini).

RX goes to TX and TX goes to RX.

Common error I have made myself.

It doesn't make sense that you "bricked your pro mini" yet could still program it just by using a different serial adapter...

Device signature of 0x000000 on a previously working board (ie, where you know there's a crystal connected because it's on the board - as the error can also be caused if the fuses say to use a crystal, but you don't have one connected) almost invariably indicates incorrect wiring.

Unless you have hot air rework equipment and experience, don't expect to be able to swap a TQFP part between boards.

Pro mini clones are like $2 on ebay. Serial adapters are like $1.50. Just get replacements, they're super cheap.

The good (IMO) ebay serial adapters are the black CH340G ones with the 5v/3.3v switch on them (not the ones with the button).

Dr. Azzy,

Thanks for the tips (sorry for my tardy reply, I'm new to the forum and didn't have email notifications enabled).

You're completely correct that the best use of my time and money is to buy a new $2 clone and move on, but I think there might be something for me to learn here. I should have (but didn't) mention that the sketch previously uploaded to this board would not run after the anomaly (whatever that was). Up until that point, I had successfully been able to upload sketches to the Pro Mini through the Uno.

Now I have the hypothesis that the clock fuses may be been reset or modified somehow. I'm pretty handy with my hot air rework station, so removed the Atmega328 from the ProMini, put it on a breakout board, and now I'm trying to read the fuse bits. I don't want to buy another programmer, so I'm trying to use Arduino as ISP to access the fuse bits of my "broken" 328.