Two things. Diving deeper into other replies and an alternative theory.
DSPOBJD OBJ(QSYS/STRTCP) OBJTYPE(*CMD)
Not WRKOBJ. If the object exists but you do not have authority to it, it will not show up in WRKOBJ. In DSPOBJD you will get notified that you do not have authority, or it doesn't exist.
DSPSYSVAL SYSVAL(QSYSLIBL) QSYS should be part of this.
I confirm that STRTCPIP is not a valid command. At least not provided by IBM. Unless in some obscure fashion, like QSYS38?
Now, here is another option:
DSPPTF LICPGM(5770TC1)
If you get "Product 5770TC1 *ALL not supported or installed." you have to install it. It is installed by default, but maybe, just maybe, someone set up a system with the barest minimum on it. Figuring you were going to scratch install from your own old system.