Some desktop CPU's do support ECC
http://ark.intel.com/search/advanced?ECCMemory=true&MarketSe...
But good luck finding a motherboard for that socket that supports ECC memory.
That said entry level Xeons are not that expensive an E3-1220 v5 costs 200$...
But if you are going for your machine it doesn't look like money is an issue.
But that said if you need that much computing power why even bother building a machine?
You can get used rackmount servers on the cheap these days, and if you live near a place that does foreclosure auctions you can get them ridiculously cheaply even if they are new in box.
Here is a server with 2 x 8 core CPU's and 192GB RAM for 1200$ and with B/O you can probably get it closer to 1000....
http://www.ebay.com/itm/Supermicro-2-x-E5-2670-CPU-192GB-RAM...
If you don't want to stick it in a closet then a 10-15U rack is also 100-150$.
And just remote to the server from anywhere you want....