What are steps to do this repair? Should I replace all broken looking parts and try to turn it on?
It depends on how you define "repair". Do you consider a "repair" as 1. "fix the broken parts", or 2. "make the motherboard work"? If #2, then you are possibly into the realm of motherboard "troubleshooting", and that is well beyond the scope of the question.
From the photo there are clearly broken parts that needs to be replace. The Y1 crystal is crushed and needs to be replaced. The 14.381MHz frequency suggests it has something to do with video since that frequency is commonly used to generate NTSC/PAL. If the motherboard has on-board video, then it most likely will not work. If the crystal is required by that UMC UM82C491F chipset IC right there in the photo, then most likely the motherboard will not work at all.
If the damaged SIMM sockets are not electrically compromised in a way that they are causing short circuits, they they will not impact you ability to test the motherboard as long as it can operated with a partial memory configuration, i.e. using the first 2 or 4 slots instead of all 8. If you want to use all 8 memory slots, then the two SIMM sockets will need to be replaced.
To "replace the broken looking parts":
*Notes: Rework, and specifically desoldering is twice as hard as soldering. This is not going to be easy. The board probably used leaded solder. Clean joints and flux makes rework "work".
Use a hot-air bath preheater on a low setting (120c to 130c) and place the damaged part of the motherboard over the preheater. Even old motherboards are multi-layer PCBs with large power and ground planes that makes seemingly small jobs very difficult. The through holes can be very tight and makes it difficult even to remove single through-hole parts.
Using 99.9% alcohol, like MG Chemicals 824-1L 99.9% Isopropyl Alcohol Liquid Cleaner, clean all the pins for the crystal and broken SIMM sockets with cotton-tip cleaners.
Using a temperature controlled soldering iron set to 330c (~640f), reflow the crystal pins with a little solder.
Using solder wick or a heated vacuum desolder iron, remove the solder from the crystal leads and remove the part. Using small pliers you can move the part slightly while heating the joint to help remove the part if necessary.
4b. Optionally use a low-temp desolder alloy like ChipQuik to lower the melting point of the solder joints. Applying a small amount of ChipQuik to the joints with your iron, mixing with the original solder will make the solder joint liquid at the hot air bath temperature.
Clean the empty holes with alcohol and reflow solder into the empty holes. Apply flux and use solder wick to cleanly remove all solder and clear the holes. Clean with alcohol. The holes should be shiny and look like they never had a part in them.
For the SIMM sockets almost certainly the ChipQuik will be required to remove them without damaging the PCB, or a heated vacuum desolder iron. Just like step 4b, apply ChipQuik to every SIMM pin to flow the existing solder and mix the ChipQuik alloy. The joints will become liquid at the hot air bath temperature, which means they will all be liquid simultaneously once ChipQuik is mixed with every pin.
Use small pliers and/or a plastic spudger to wiggle and gently pry the SIMM socket. Check for pins that are not liquid and mix ChipQuik with your iron as necessary to free every pin. Remove the SIMM socket.
Clean all SIMM socket holes as done for the crystal in step 5. ChipQuik is hard to clean with wick, and is easiest to clean while the hot air bath is still on, using cotton-tips and alcohol. However, the holes still need to be cleared by reflowing with fresh solder and wicking. This takes time and patience or you will pull pads and damage the PCB. This is also one of the hardest components to remove, and not for the feint of heart or beginner.
Turn the motherboard over and clean the tops of the holes and inspect for damage.
Install new parts and solder. Again, since many of the pins in the SIMM sockets will be connected to power and ground planes, I recommend using the hot-air bath to help resolder the parts.
For removal you can optionally try using a hot-air station, but it is hard to keep all the pins at liquid temperature due to the size of the socket, while at the same time trying to gently pull and pry the socket out. It will be very hard to use hot-air without three hands (or an assistant), and without doing damage to the PCB.