I can't figure out how to articulate the underlying rules here very well.
Hopes is a plural noun here. In the first sentence, "to build" is an infinitive, the root "to" form of a verb. "Building" is a gerund, a verb that has been turned into a noun.
You can say this with the infinitive, in which case you need to change "hopes" to a gerund:
Some geek wannabes welded parts of the robots hoping to build phones, radios, and armors.
Or you can use the gerund, in which case you should pick either "in the hope of" or "in hopes of."
Some geek wannabes welded parts of the robots in the hope of building phones, radios, and armors.
Some geek wannabes welded parts of the robots in hopes of building phones, radios, and armors.
There doesn't appear to be a clear "right" version of that phrase, but those two are the most common. https://english.stackexchange.com/questions/97795/in-the-hope-of-vs-with-the-hope-of