The main quirk and problem with having no digital search is that all advances in computing past the 1950s/1960s wouldn't be possible.
This is roughly when computers stopped having their execution controlled by a physical setup, such as card with holes punched in it or a system of levers, and started being controlled by a set of instructions loaded into memory - the magnetic hard disk drives we use today are the modern extension of this.
Having no way to search for digital information stored on a drive essentially means you have to look at the entire contents in sequence, which takes longer and longer the larger the available memory, and thus puts a limit on the size and complexity of any computer.
This also makes writing an app difficult.
To see the real world effects of this we can simply look a few decades into the past:
- Libraries still use physical index card systems to catalogue
- Phones can still be used - early systems used switchboards manually controlled by an operator which connected you to the line you wanted to reach. Later, phonebooks contain lists of all phone numbers you can dial to reach some endpoint.
- Encyclopedias would be relevant again, as they're essentially a
collection of commonly needed information in book form. Books would definitely be more prevalent
- Physical maps tell you where to go
If a way to develop and host a website were developed using the restricted computing technology available, we could end up with "websitebooks" too, a physical listing of all known web addresses.
However, in reality (as other people have mentioned) eventually someone would realise there's something missing and connect the dots.