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I don't know the first one but the second is definitly Mister Mosquito for PS 2.
http://en.wikipedia.org/wiki/Anime_Unleashed
^List of anime that aired on G4. The fact that you said arcade made me think of http://en.wikipedia.org/wiki/Magical%E2%98%86Shopping_Arcade_Abenobashi
. If I remember, each episode was a different genre, so there might have been a giant robot episode.
It Might be one of the Machine Robo Series, putting in Arcade Machine Robot Anime dinged it so it's worth a shot...
It says the most recent version was in 2003, but it goes back to the mid 80s so it's entirely possible Tech TV might have broadcast SOME version of it.
Wait, I'm an idiot. It's definitely Betterman. I can't believe I didn't get that, it's a personal favorite of mine. Keita and Hinoki wake up on a beach after the credits, the only members of the cast to definitively survive the Bestman/Algernon debacle.
Edited by EponymousKid

I have 2:
1. Anime with giant robots, and the main character is kind of nerdy and socially awkward. In the last episode all of the characters wake up on a beach, and as soon as they see they're all alive they start laughing. also, there was an arcade game that would help them control the robots or something, I don't know. If it helps, this aired on g4 when they still had their anime block.
2. A video game which involves being a mosquito.
Edited by originalhobbit