I'd say a keyboard that's that awful inside isn't worth the effort to reverse-engineer... the Adesso one (also sold as a SolidTek) had separate connectors for rows and columns, as typically do the super cheap (and sometimes, but not always, awful) eBay ones such as I'm using in the AnyTop.
For the record, the AnyTop has the same specs as the cheapest laptop at my local Wal*Mart... which is a $219.xx HP job that honestly looks like it should say Tonka* on it somewhere. Cheap bright-blue and white plastic... it's horrendous, and it really does literally look like a kid's toy the way it's put together.
*For those not in the know... Tonka is/was a popular line of toy trucks for little kids, along the lines of Hot Wheels / Matchbox / etc. Not remote control or electronic at all -- just little push-around cheap plastic toys.