Many MacBook models will not power up if the battery is basically dead. And, reading between the lines I'm assuming this is an older model MacBook which probably still has its original battery - and therefore at much greater risk of having a dead battery.
You could try powering the MacBook up while connected to AC power and without the battery installed (this was possible with some models), but otherwise you'll need to replaced your battery (something I would recommend even if you could power it up without the battery).
Most MacBook batteries have a life expectancy at or around 1000 cycles. It's not uncommon for batteries to exceed or fall short of this number; it's just an estimation of how long it can last.
Your options are to have the battery replaced or to only use it while connected to an AC power source (if this works for you). There are many 3rd party battery options available for purchase, so if you're still happy with your MacBook then that's your best option. If not, then it's time to upgrade.
If you do decide to replace the battery, then I would ensure that you purchase a battery from a reputable online store dealing with Apple products.
For example, the following are some well-regarded sites:
By buying from a reputable store you'll be sure to get a battery fit for purpose, regardless of manufacturer. Being reputable means they're only going to sell something that works and they'll stand behind the product they sell, regardless of the brand.