You need to open new accounts. Your manager helpfully reminds you from time to time. In a perfect world you would send a letter of introduction, follow up with a phone call to schedule an appointment and meet face to face. None of that seems to work anymore. You call and leave a voicemail that never gets returned. What can you do?

1. It is not what you know, but who you know. Figure out who you know who also knows the decision maker you want to reach. You might do this using LinkedIn, by searching on their name and seeing who 2nd level connections are. If you see the name of a friend, call and ask how well they know the person. If it's a good connection, would they pick up the phone, call the prospect and ask them to give you 10 minutes?
2. Here is another way to use LinkedIn. It is a small world. Your target company likely has more than one decision maker. Look them up on LinkedIn. See where there are 2^nd level connections. Send a personalized invitation to the people with 2^nd level connections, referencing your number of shared connections. Is there a reason why it's worthwhile for them to connect? Once they have connected, revisit the other key names that were 3^rd level connections. With the addition of the new connection, they might now be 2^nd level connections. Repeat the process.
3. The old school tie. You graduated from a local college. You still keep in touch with some classmates. You attend the alumni events. Do an online search through the alumni directory. Which alums work at that company? You have a better chance of them accepting a call from a fellow graduate. Do they know the person you want to meet?  Can they help you make the initial connection?
4. Go where they go. Let us assume one of the national HR professional organizations has a local chapter and you have joined as an associate member. If not, maybe you belong to the Chamber. Does the person you want to meet also belong to the same group? Can you walk up and meet them at an upcoming meeting or event?
5. Send a letter of introduction by overnight mail. Express mail was started in the late 1970's. It's been around awhile, but it still conveys a sense of urgency. A simple explanation is the recipient realizes "Someone was willing to pay about $27 to get my attention."  If you call afterwards and remind their assistant you sent the overnight envelope, they should remember it. That is a start.
6. Call outside office hours. This makes sense if you are trying to reach a business owner. They often work long hours including weekends. Their screener does not. Many business owners are hard-wired to not ignore a ringing phone because it might mean new business. You might be calling at 7:00 a.m., 7:00 p.m. or 10:00 a.m. on Saturday, but it shows you work long hours too.
7. Will a charity or nonprofit introduce you? Years ago, a national nonprofit running its campaign in a major city explained they try to help donors when they can. Top donors might be invited to an exclusive reception. They are often key decision makers at their firm. The development officer explained they can help facilitate an introduction, since both people are each helping the organization in their own way.
8. Do they play in a golf tournament? Many nonprofits and charities hold golf outings as fundraising events. These are social events for businesspeople. Since people are organized into foursomes, have cocktails and enjoy dinner afterwards; there are opportunities to connect.

There are many ways of getting on someone's radar while maintaining a professional demeanor. You can always walk into the business and ask to speak with the owner too.