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i have never had much luck with wick for anything other than cleaning solder from the pcb connector after some asshole has soldered a jamma adapter directly to it or tried to raise the surface to counter a worn edge connector.
that second example seems relativly common on space invaders or atari stuff.
(a new edge connector would have been better!)
This is about my experience, it did work really well to clean the solder off a Contra bootleg that had had several AMP connectors wired up to it to connect to a cab

On my previous work, we had a tweezer sort of desoldering iron that had both legs heated. You could mount some L shaped tools that desoldered 2 sides of such a chip simultanously. First, you had to bridge all the pins with a lot of solder as you didn't wanted one to stick to it's pad when you lifted the chip. Such a tool and maybe some chip quick might be able to do the job. After that, you will need to clean the solder pads with desolder wick and remove the excess solder from the pins of the chip.
Next is getting those straight again. Personally, I would try to find and install a new chip.
I do know about soldering tweezers, didn't realise you could get an attachment like that though, may have to look into it.

A totally new CPU is a great idea if it's not custom and/or impossible to find, I'm not entirely hopeful the CPU on there currently is good (if it's been plugged in like it is now the CPU will be fried) - the problem is I have no idea what it actually is.
 
It's an R4600 MIPS CPU, these were used in other things but not as a QFP package generally. Will need to do some research and see what I can find, I did find one on eBay but for far more than I'm willing to risk.

Like most CPUs they are mostly found as a PGA for installation onto a motherboard
 
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