The Sony HB-F1XD features a very similar video/audio daughterboard. Since the circuit is pretty much standard, you can probably use this service manual as a reference.
From the following picture, I can see that the pin-10 and 11 of the CXA1145 were badly affected by the corrosion, and those are the CYNC-IN and CSYNC-OUT respectively. You should check these connections carefully. Also check if the Vcc1 (pin-12) of the CXA1145 is properly connected.
check solder of IC's on mini-board before replace capacitors
Hey Folks,
Finally got some time to look at the FS-A1 again, got a big magnifier and a good flashlight and surely enough I found some eaten traces, few hours of soldering and I finally got an image 
The video output comes from composite (easy to test) but it's not complete yet, it's missing one or two layers of sprite.
Massive thanks to everyone for bringing me to that stage, was really busy with other things but finally it's working
Here is a video, let me know your thoughts:
Congratulations on getting this far! Close now to get it working again .
Check the VRAM lines next… There’s a problem with the connection of the VDP to the VRAM or the VRAM itself, causing the missing sprites and weird characters in Basic. Data lines to VRAM chips 0-3 by the looks of it. Check line 3 first, that one’s definitely not working.
Congratulations on getting this far! Close now to get it working again .
Check the VRAM lines next… There’s a problem with the connection of the VDP to the VRAM or the VRAM itself, causing the missing sprites and weird characters in Basic. Data lines to VRAM chips 0-3 by the looks of it. Check line 3 first, that one’s definitely not working.
Thank you very much, I'm checking the RAM lines, I've noticed that the RAM chips get really hot is that normal? 2 out of the 4 are really hot the others not so much. I'm not leaving the computer very long as a result just in case
Quickly identified .