I called a repair shop and they told me that the primary internal battery is NOT the removable battery 0n the back of the computer, but an internal battery, hence the name. Is that true? They then told me that the don't sell batteries for a HP Pavillion Touchsmart 14 sleekbook anymore because it's outdated. Does this sound correct or should I not give up on fixing my laptop? Thank you!
How have you detected the battery won't hold a charge? At your desktop, what does the battery status say? If that isn't detected (or appears to charge, but won't hold)..... then that's the removable battery.
Laptops don't (generally) have CMOs batteries like desktops do, so I'm not very sure what battery they would be alluding to.
You'd have to verify your specific model, but a battery should be easily sourced for $20-$25 max.
Is this a Celeron based laptop? It's probably not too usable for most people but, if it works for you, and a replacement is going to cost more than the cost of the battery, there's certainly no harm in replacing it.