I don't think you will find a raspberry PI competitor for the $35 price that has gigabit and SATA. There are some similar form factor with gigabit but they are $75+ Your best bet would be to go to a pawn shop, thrift shop or similar and buy an old desktop.
The only candidate I can find that is close to your desire is the RockPro64 which has gigabit and PCIe x4. That would be enough for SATA.