The answer is you should rely on neither your old laptop nor your new one. The wallet you have installed on both of these devices just gives you the ability to interact with the blockchain, but it would not be possible without something called a seed phrase that has real power. It is the seed phrase that ensures you have a right to certain pieces of information stored on a blockchain, and it allows you to create cryptographic signatures proving your ownership over the funds. As long as you keep your seed phrase in a safe place and only touch it when you need to export to a new wallet, you retain control over cryptocurrency and thus should not be worried. You can have a single secret key (your seed phrase) and an unlimited number of devices on which this secret was used to create a wallet. If some of these devices get dysfunctional, you can create a wallet on some other and regain access to your funds on the blockchain.