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I was wondering how likely it would be for me to get a job as a patent agent or something with a bachelors in EE and having a firm sponsor my tuition. I would like to go attend one of the following: Columbia, Harvard, Stanford, Penn, UVA, Chicago, NYU, or Berkeley. My GPA is roughly 3.7 (top 15% of class), and would be higher if I didn't have a death in the family that caused me to do poorly for a semester. I'm PTing low 170s right now and will retake if it is not higher than 172-173 range. Although if I had a company sponsor the costs of attending law school would I need to work there for a year or two beforehand? Does anyone have any experience with this at all? Ideally I want to get into a big law firm in California or NYC.

This isn't terribly common but I suppose it can't hurt to try. Have you taken the patent bar yet? If so, you could apply to patent boutiques now, although you probably should wait until you have been admitted to a nearby school. Finnegan in particular has a program to sponsor law students (see their web site); they are focused on part-time programs, but also do full-time programs at Harvard and Stanford (where Finnegan has offices nearby the campus).

You have a good shot at getting into some of those schools depending on LSAT score, but none are a lock. Schools won't care much about the GPA excuse. They mostly care about numbers.

The upside is financial. The downside is that you will basically be committed to the firm sponsoring you, unable to try other firms out when OCI comes around, and too busy to focus on getting good 1L grades (which are important if you want to switch jobs). It's also hard to find a gig like this.

I'd say this is rare enough that you shouldn't count on it.