my streaming stick seems to be broken. When I turn on, the purple Roku screen starts and the colors are off. Then, the entire screen turns a yellow gradient for about 10 seconds and then there is no picture or signal.
What model Stick do you have? If you can't see a model number embedded in the case somewhere, is the case purple?
A purple case means it's the 3400/3500. That version of the Stick is basically obsolete. It doesn't work with some of the newest channels, it's lacking in power, and replacement remotes are no longer available. If yours is purple and you still have a working remote, you can probably sell the remote for enough to pay most of the cost for a new one.
If it's not a purple case, it's a 3600 or newer, and they are still a reasonable player. However, from the description of what you are describing, it's very possible that either an internal component has failed, a crack in a solder joint has broken a connection, or some other failure has occurred. Considering the cost of a new device, there's no logic in attempting to repair it.
Dan Roku Stick (3600), Ultra (4640), Ultra (4670), Ultra (4800), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.