As a minority shareholder in a closely held corporation, your rights will be defined by the governing corporate law (in your case, that of Illinois) and by any charter documents or agreements that may create contractual rights of some kind.
Above all, see a lawyer in your local jurisdiction to get advice on this. I am a lawyer but obviously can't give legal advice in this type of forum.
In the abstract, however, the following principles tend to apply:
1. Shareholders in a closely held corporation generally cannot force the company to back back their shares. Exceptions exist - for example, if you have a shareholder agreement in place that gives you such a right or, in some states, you might have what is called a "statutory close corporation," which can have intricate contractual provisions defining its corporate structure. Check with an Illinois lawyer on this.
2. Minority shareholders generally do not have a right to inspect board minutes (again, your local laws may vary) but do have a right to get annual financial information and to inspect certain other corporate records.
3. When you received your shares, you may have signed documents giving the company or other shareholders a right of first refusal in the event you attempted to sell or transfer your shares to a third party. If you did, then you will need to first obtain an offer and then first offer the shares to whoever holds such a right on the same terms before you can sell them to the third party.
4. Securities laws generally also forbid any immediate resale of the stock. If you have held the shares long enough, however, you will normally be allowed to resell them absent any specific restriction such as a right of first refusal. However, the market for illiquid shares of this type is usually nil.
5. It is usually very difficult and expensive to enforce legal rights as minority shareholders. Many states prevent you from filing suit directly against an incompetent management. Even if they are doing things wrong, your remedy usually is to file what is known as a shareholder derivative action, which means suing in the name of the corporation to try to recover monies for the benefit of the corporation. A derivative action tends to be a clumsy and expensive vehicle for most minority shareholders unless it is an unusual situation where the stakes are high. On the flip side, some minority shareholders will use this as a way of harassing the company until it is motivated to get rid of them - it sounds like you have grounds to file such a suit, but you will need to be able to fund it.
6. You can insist that the company hold annual shareholder meetings and give you whatever information your state law requires in such a meeting format (usually, it is a basic financial report). If they refuse to hold an annual meeting, you can sometimes complain to your state's corporate division, which often has an enforcement arm having special powers to compel such meetings.
7. If you hold a specified minimum percentage of the corporation's stock, you can file an action for involuntary dissolution of the corporation. In California, this number is one-third or more of the outstanding stock. Check with a local lawyer to see what you need in Illinois. In an action for involuntary dissolution, provided you can show grounds, you can get a court to force the sale of the company's business or otherwise to force a distribution of its net assets (or the value thereof) to shareholders.
Having said the above, if you and the others hold at most a few percent of the company, you are likely stuck as far as what you might be able to do practically through formal legal remedies. Before concluding this, though, do the record inspections and consult with a lawyer.