How does someone contact Central Beijing's departments?
Is there a website with each department listed?

Do you mean the municipality of Beijing or the central government of China?

In Beijing, the districts have a lot of departments and policies are not consistent one district to another.

Best way is to do a lot of searches. Clearly results depend on the search word(s) or phrases.

The next problem is finding gumbment websites that are updated and current.

Finally, no one seems to answer phones or emails. Contacting departments usually means a visit and guanxi really helps if you can get introduced.

"Contacting departments usually means a visit and guanxi really helps if you can get introduced."

A friend just told me that where she lives she no longer needs to bribe the officials to get her official documents done. She said that this was bcs of recent policies and was thankful to that.

Yes, guanxi certainly helps. A 'nobody' will still get the 'nobody service' although bribes may be in the past.

I'm looking for a website or directory of Departments for China central government.

That is a good question. I have never found one. This site will answer questions, so they say:

onestop.globaltimes.cn/

Here is a complete list of Chinese Ministries (I think)
If you google any one of these and get the wikipedia page, scroll to the bottom. The first link is usually the official site. They often have English language pages and an 'contact us', 'hotline' or 'inquiry' section:

Name of Ministry:

Ministry of Agriculture 农业部

www.agri.cn/

english.agri.gov.cn/

english.agri.gov.cn/hot/

Ministry of Civil Affairs 民政部
Ministry of Commerce 商务部
Ministry of Culture 文化部
Ministry of Education 教育部
Ministry of Environmental Protection 环境保护部
Ministry of Finance 财政部
Ministry of Foreign Affairs 外交部
Ministry of Housing and Urban-Rural Development 住房和城乡建设部
Ministry of Human Resources and Social Security 人力资源和社会保障部
Ministry of Industry and Information Technology 工业和信息化部
Ministry of Justice 司法部
Ministry of Land and Resources 国土资源部
Ministry of National Defense 国防部
Ministry of Public Security 公安部
Ministry of Science and Technology 科学技术部
Ministry of State Security 国家安全部
Ministry of Supervision 监察部
Ministry of Transport 交通运输部
Ministry of Water Resources 水利部

Thanks Scally

I think Scally does have the 20 Ministries all right.

Here is a more comprehensive list of government departments:

english.gov.cn/[...]