Should I change my battery? I Have a MacBook Pro (13-inch, Mid 2009). Now the battery status is "Service Battery". I'm thinking of getting a new Laptop. 

My question is can I use my laptop even battery is dead by plugged in? 

Or 

Should I change my Battery?
You can continue to use your MacBook Pro by always having it plugged into mains power. This approach will work and work well.

I use an older MacBook showing "Service Battery" at home. It is always plugged into mains power. The computer works well and does everything my family need of it.

Ask Apple for a Quote

Before buying a new laptop, ask Apple how much a new battery would cost. The cost will be significantly lower than a brand new computer.

Replace the Battery Yourself

Alternatively, iFix provide instructions for replacing the battery yourself but Apple do not recommend this. Apple do not recommend this because incorrectly fitted batteries can be dangerous and they can be a fire hazard.