How to get expenses to show on a Profit and Loss statement and/or in the chart of accounts?

"I entered my income and expenses via my check ledger, petty cash ledger, and credit card ledger under accounts."

You can work in the ledger or Register view, or work in the actual data input screens of Write Check and Enter Credit Card Charge. There are more data fields available if you use the full view of the transaction and don't just work in the Register.

"When I try and make a profit loss statement it doesn't report any of my expenses except for one that I made by a general journal entry."

Actually, you hardly ever use JE in QB.

And we need to identify if the Expenses are dated in the range of that report. And, are they really Expenses, or Expenditures for things like Computers and Inventory? Assets do not show on the P&L. What do you see when you run the Balance Sheet and the Statement of Cash Flows?

"It has my income on the statement and COGS."

What are you posting to COGS? That is expense.