A friend of mine got some bitcoins a few years back, now he told me he can't operate with his old laptop (hard disk capacity issues, I guess he can't dowload the whole blockchain, and I say I guess cause I started reading about bitcoins just yesterday, to try to help him with his issue).
This is different question, so you should have posted a new thread, but here is one solution for your friend:
You do not have to buy a new computer. You can just get your private keys from the old bitcoin-core without needing to download the whole blockchain, and then import those keys to electrum, which will work in the old machine.
More info here:
https://bitcointalk.org/index.php?topic=2250550.msg22754328#msg22754328