Error:Connected system timestamp not found on target at expected base address.

Yes it looks like there is something in the FPGA that is working, at least. Be sure you don't close the opencores evaluation window as it will make the CPU stop and won't let you read the system ID.

You can try and open System Console and use it to read directly the two registers from the System ID component and check what you get back. You can start with

set mast  0]
open_service master $mast

and then

master_read_32 $mast 0 1

should give you the ID and

master_read_32 $mast 4 1

should give you the timestamp.

Are you sure the Timestamp ID component is connected to the Nios CPU's data master? Is it on a different clock domain? If yes is this clock running?