I've never replaced the network board in a Panasonic, but I did own a 2010 Panasonic Plasma similar to yours (a G20) and had a similar issue after a couple years. I would press the "Viera Cast" button on the remote and get nothing. The screen would flash for a second like it was going to launch into the app page and then nothing. Since I never used the apps built into the TV much anyway, I never bothered to fix it.
If I recall correctly, no Panasonics came with a wi-fi adapter in 2010 and it was an optional accessory. the appropriate adapter was the DY-WL10. There's also a generic Netgear adapter that works with 2010 Panasonics that should be easier to find...the WNDA3100.
ht Panasonic 60" ZT60, Monitor Audio: Silver RX6, RX Centre, Radius 90HD; Martinlogan Dynamo 700, Marantz SR5006, PS3, Oppo BDP-103D
2ch Sony KDL-32W650A, Sony BDP-S1000ES, Marantz PM8004, JVC T-X3 tuner, Monitor Audio Silver RX1, REL T3, Apple TV, Peachtree Audio DAC•iT, Sennheiser HD598
lr Panasonic 50" ST60, Sony BDP-S5100, Apple TV
pc Energy CB-5, Audioengine D1, FiiO A1