Dell Latitude 7300 fan not working properly

Hi,  

I have a Dell Latitude 7300 and the fan is acting strangely:  

- Fan does not spin during normal use or boot  
- When the laptop gets hot, the fan sometimes suddenly spins very fast  
- After cooling down, the fan stops completely  
- When the battery goes to 0%, the fan spins for 2–3 seconds before shutdown  
- Moving the fan connector a little can make it spin at full speed  
- Sometimes after shutdown, the fan keeps spinning at high speed  
- Dell diagnostics show inconsistent fan readings  

**What I tried:**  
- Fan is brand new and clean  
- Tested fan with 7V outside laptop → works fine  
- Fan spins freely by hand  

I’m not sure if it’s a motherboard problem, fan connector issue, or something else.  

Has anyone seen this before or knows how to fix it? Thanks!