Google-sheets – Conditional formatting based on another cell value

The ISBLANK formula should serve your purpose well.

Create a new rule in the conditional formatting menu. Set the range of your rule to D2:D so that the formatting is applied to column D. Then, in the Condition dropdown menu, select "Custom formula is." In the input field, enter =NOT(ISBLANK(C2:C)). (The = implies the rest is a formula. The NOT formula negates the value returned by its argument. Since you want the formatting rule to apply if the corresponding cell in column C is NOT empty, you will need to use this.) Finally, set the formatting to suit your needs.

Unfortunately, you will need a conditional formatting rule for each team (not cell, though), as you can only set one fill color per rule. Assuming you want to format based on the value of an entire cell rather than a substring, then in each of your rules, set the condition to "Custom formula is…" and then enter =($B1="Team 1") (replacing "Team 1" with the value you wish to color with a given rule).

Make sure you include the equals sign at the beginning, as that tells Sheets that you are entering a formula. Also be sure to include the dollar sign ($) before the letter of the column of teams—I assumed it is column B based on your image—so that it only looks at the value in that column when determining whether or not to apply the formatting. (Using the dollar sign there turns it into an absolute column reference.)