You've got some lifted and damaged tracks and pads.
I can see some in the photo of the underside of the board:
The damage I can see is indicated by the red coloured arrows.
With any luck, you have not destroyed the plated through hole connections. So what I suggest is the following:
Download and print out a schematic (circuit) wiring diagram of your machine. All the following tests are to be done with the machine disconnected from the mains power and from any other devices.
Using a multimeter on the continuity range, (or on the 200 ohm range if yours does not have a continuity range), test between each of the ROM chip pads (pins) and other chips that you have not worked on (for example, the CPU). Do this for the ROM chip pads (pins) on both sides of the board, and for both ROM chips. If the test is okay (meter bleeps or shows less than 5 ohms) Mark the relevant circuit on the printed out schematic with say, a tick in green or blue pen. If you don't get good continuity, mark it with a red cross. If the schematic shows the circuit going to many other chips or components, it's worthwhile testing at least as many other points as you can. As the tracks on a circuit board do not follow the layout of the schematic.
Where the track / pad is good on the top, but damaged on the underside of the board, use some very fine tinned copper wire (like very thin fuse wire, or wire strands out of a flexabe cord (cable). Carefully wrap it around the relevant pin of a new DIL socket (one and a half to two two turns) and apply just a little bit of solder. Leave plenty of spare wire, cut and do the next pin. Repeat as required. Then thread each of the wires through the relevant PCB holes followed by inserting the socket. Note plan ahead and do the sockets in a suitable order, so that you can still get to the relevant top (component) side pins of the sockets with your soldering iron.
Now solder the top side pads on the socket where you have your fine wires. Then solder all the underside holes where the pads are good. When the pad is lifted, if possible, see if solder will still take to the plated through hole. If the track to the pad is broken or the pad has lifted leaving no conductor to a track, if the gap is small, you can carefully scrape off the solder resist (green in colour on this board)m tin the exposed copper track. Tin the wire once cut to the correct length. Then quickly and carefully solder the wire to the track. Use a flat bladed screwdriver to hold the wire (unless you like pain).
Good luck Mark
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Falcon, Atari 520STFM, Atari 1040STE, more PC's than I care to count and an assortment of 8 bit micros (nearly forgot the Psion's)