The charging port on my Acer laptop is dead, I thought it was the charger but I bought a new universal charger only to discover that the problem was the port on my laptop. The new charger has USB ports on it as well as different size heads, can I charge my laptop using the USB port since my charging port will not work?
No, it won't work.
The USB ports on the laptop can only "send" power, that is, they can be used to give power to other devices (such as mice, keyboards, mobile phones…). Those ports CANNOT be used to receive power.
A laptop charger delivers around 19V at 90W (varies with each model).
A USB port used for charging delivers 5V at 500mA up to 1000mA or 2000mA.
So, the voltage is completely different.
Doing some math: 5V × 2A = 10W
So, the best USB charger out there can only deliver 10W, which is not enough to keep a laptop powered on.
Footnote: are you sure that your universal charger is not broken? Are you sure you have set it correctly, regarding the voltage and the polarity?