I have one word for you: maintenance.
For something to be indestructible for that long it has to have a system of maintenance. And those have to have back up systems, as well as back ups of those back ups.
Just the BUILDING your server is in is going to need maintenance.
Stuff needs replacing, even in the future. Foundations crack.
So you will need nanites, and you will need robots or androids, or else it won't be pretty.
Robots will also need to be repaired and maintained.
Your server will be indestructible in that it will be maintained and protected. The idea of just leaving it be without that..you need to watch Life After People.
Your scale is 10,000. Even with advanced materials which do not yet exist on earth, destruction happens, unless you maintain.
So, what you will need is a series of failsafes in place. And you don't want to think single server here--over 10,000 years, that way lies death. Everyone knows you always have a back up...
1) General blue print for the whole system is present in all maintenance droids.
2) Droids should be in locations other than just one.
3) There's a planetary defense system for objects from space.
4) Multiple memory caches rather than just one. If one fails, you have back ups. There could be a relay system with old copies of the system. Scary bit is that people could lose time and not know it, because everyone has lost time--because the server in one location is destroyed or isolated, for one reason or another.
5) There will be mining for raw materials and a supply chain, because it will be needed. Earth will be easiest, even if they are bots, because we have a variety of materials, and conditions easily allow for construction and things like blow torches. Another planet's not out of the question, but Earth has too many advantages to ignore. (Although there are liabilities such as flooding that might not happen on a planet without water--but it will be a planet without water. And you'd be surprised how useful water will be in maintenance.)
The goal is 10.000 years a very long time.
Natural disasters could happen all the time, so the server should survive these You would need a complicated predictive modeling system in order to prepare for those via maintenance bots.
Where would we put the server? Underground is best. But one location is not a good idea.
What protection will it get? (Just buried under the earth?) Active defenders in the bots.
What components would be used to make it near indestructible? There's lots of bleeding edge tech in this area, carbon nanofiber, self-healing concrete are place to start, but microscopic maintenance might be a bigger help than the creation of materials.
This world is set in a semi-far future, and we could place it anywhere in our solar system, so not just the earth Earth will make things more and less difficult in ways I have outlined above. We are used to working in our own gravity and atmosphere, so it would certainly be easier to build an efficient system on our own planet for something this advanced.