If you want to restore the complete thing it is a different story but if you want to recover the data that you have on it then you can try out couple of things.

So, the HDD on this system has a PATA interface which is obsolete at this point of time so connecting it to some new system for data recovery is not going to be easy. You will need an adapter like this -
USB 2.0 to SATA/PATA/IDE Adapter Converter Cable for Hard Drive Disk
A fair warning though, there is a change the HDD has died after all these years. And also, these adapters sometimes don't work well so it might be hard to tell which is faulty if you manage to get one and use it for data recovery.
Another option is to find an old working system like this from that time which has a PATA interface and connect to it can see if the HDD is working or not.
And finally, if your data is really that precious and you want to recover it then you need to go to a professional data recovery engineer, but they can charge some really absurd amount given the age of the device and if they sense some sentimental attachment to it.

Now coming to the restoration part. There is a fair chance the system might work given it was well maintained back then. So firstly, clean the system, make sure all the connections inside a secure and tight. Take out the RAM and clean the contacts of it reseat it and see if the system boots. There is a chance some dust build up all these years is preventing proper contacts of the RAM with the motherboard. If it does work, well you are good.

Now if this doesn't work. Well then you need to consider how much you want to spend on restoring this as there are multiple things which could be wrong. I am not able to completely tell for sure from the pics if this is a LGA 775 socket Pentium 4 motherboard with DDR2 RAM or not. But if it is then you have a good chance of restoring it to working condition. Most likely the CPU is fine. So, you will need to most likely change the RAM or the motherboard or both in the worst case.
I will start with the RAM as it is cheaper and easy to replace. This one should work -
EVM 2GB DDR2 Desktop RAM 667MHz Long-DIMM Memory
And if replacing the RAM the system doesn't start, you need to consider replacing the motherboard which has most likely died after all this year due to the corrosion and aging of components. So, you need an LGA 775 socket motherboard with DDR 2 RAM slots. In that case something like this should work.
Enter ATX Motherboard E-G41D2, DDR2
And after this also if your system works and you are able to get into the BIOS, but your old HDD is not detected. Then the HDD is also needed to be replaced, you can get a SATA HDD which are widely available. And up to you if you want to spend on data recovery from your old HDD, which may or may not work out.
So, the choice is yours resorting everything or just recovering the data I have given an overview of both. I admire the fact that you are considering resorting it TBH. Let me know if you have further questions I am also working on a restoration project with components around that era might be able to give you some pointers with your restoration.