You can usually get a generic laptop battery that works well for $30, if you've got a laptop with a replaceable battery.
The laptop seeming slow is probably either being loaded down with lots of programs running in the background, or overheating. You can look at what's using the CPU or using lots of RAM in the processes tab in Task Manager. Sort the list by CPU usage, RAM usage, drive usage, etc. If something's got weirdly high usage, look into what it is.
Tools like Speccy will show you the computer's temperatures, dust and dead fans can make it overheat which will slow things down.
After looking into that, I'd just upgrade the laptop's hard drive to an SSD for $30 at the minimum and you'd be surprised how faster it seems.
But all this does depend on how old it is.
What CPU does it have? What's the max RAM it can have? What OS is it running? Can it be upgraded to Windows 10? A 4 year old laptop should be perfectly usable still.