I just happen to have the AVD-C70ES service manual, since I own an AVD-C70ES. It appears that the part that you are looking for is as follows:
Ref. No. Part No. Description 351 1-477-263-11 PICK-UP UNIT (TDP022W)
You may purchase the replacement part (A4713410A) for $103.01 at
https://servicesales.sel.sony.com/ecom/accessories/web/index.jsp. Use the Part Number search to locate it.
Have you tried all types of discs, CD SACD, DVD? Once I tried playing a DVD to no avail. I then tried all DVDs that I had and finally found one that worked. I then tried the other DVDs again and they worked. It seems that the unit features an auto calibration routine, because the unit corrected the problem itself.