You really don't need Oscilloscope to get into computer repair, it end up more likely becoming a door stop, or expensive paper weight and if you have to ask, then you don't need it. Learn the basics first. Like how to replace LCD screens on tablets, phones and lvds connectors on mainboard, as with apple laptops to much current on one pin end up melting the connectors and shorting rail to ground, so is a common issue and then people break the power jacks, or USB mini jacks on various devices, so another common issue your come across a lot. Learn how to clone hard drives, or SSD drives and how to remove virus without having to wipe out drive, testing and replacing memory. For component repair, you need basics component knowledge and troubleshooting skill and be able to read and understand schematic diagrams as you se a lot of defective buck DC/DC controller and resistors that go bad on main board. Then you have to know how to check ESR on capacitors and absolutely need a ESR meter to start with, as they use low hour rated cheap capacitors and they go bad in power supplies and motherboards. Not all capacitors will bulge out and vent. That will cover most standard repairs.
To do most advance repairs at component level, is where you start to making good money, but you really do have to know what you are doing having extensive knowledge in circuit design and troubleshooting and invest in other equipment and a BGA rework station which is a whole another science to learn, as even for more common issues of crack solder balls under BGA. You have to be able to source new chips, as you can't use old one as substrate material and heat was the issue, using old chip it will just fail again and know how to set temperature profiles for ramp up and down and ETC. So you don't damage and warp board and for humidity control to get a successful replacement of the chip and reball done. One profile is different from another, as a lot of factors you have to consider when creating a good profile. I use to SMD rework by hand with just a heater with glass to use as a preheater and heat gun back before rework stations were popular. and can solder most chip by hand in seconds, took a while and ton of practice to become good and am a EE.