While I am not licensed in Wisconsin, your issue is one that deals with general legal principles that are similar to my state (and mainly deals with federal trademark laws).
With regards to a college's trademark, the trademark issue is not related to "state" - since this is a descriptive term referring to the geographical location. In this respect there are over 50 "State" colleges - most of the 50 states have a state college and there are others - such as Chicago State and South Florida State, etc. But their trademark rights are not in necessarily in the "State" but in the combination of the word "State" (as well as the other words, how it is written, what color is used and/or its use with a mascot. In short, your product does not necessarily infringe any particular college's trademark.
However, while you are astute enough to realize you may have a problem with public universities, you may also have a problem with other trademark holders - I know of a "solid-sate" and "State of the art" trademarks for lights and LEDs. So, you need to investigate your use of "State" further before investing your resources.
You should consult a local business/intellectual property attorney to discuss your options.
This answer is for informational purposes only and is not intended to be legal advice nor does it establish an attorney-client relationship. Please consult a local business lawyer to obtain legal advice that is tailored to your circumstances and facts. Good luck to you.
Before developing and selling this product, you must retain qualified IP counsel to address this issue. Chances are that you will need to obtain licenses from colleges and other trademark owners. Trademark violations can lead to serious adverse consequences for you, which you should avoid. On the other hand, in these difficult economic times, it is likely that you can obtain licenses on reasoanble terms. The job of an IP lawyer is to advise you about these issues and help you negotiate the licences you need, It is unimaginable to me that anyone who intends to go in to this type of business could do so successfully without retaining competent IP counsel. When you budget for the costs of doing business, make sure you include in the budget the cost of IP counsel---this is an essential cost for any business such as this.
If you copy a college's "trade dress," meaning it's school colors, general look and shape of its name's font, etc., and target its students as your customers, the school could claim that your product evokes their trademark and that their customers are confused about your product's source. So even though the word "state" is free to use, and even though you're allowing your customers to add a colored backlight LED to the product, if your product creates consumer confusion, that's trademark infringement.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.