I came across a roku 3500 which I never bothered to set up before now. Unfortunately I've lost the remote. Can I order a new one?
If I was in that situation, I'd head to Walmart or Best Buy and buy a Roku Enhanced Remote. It's $20. [EDIT: Next comment indicates I'd be wrong. So, if you follow my advice, keep your receipt.]
Now, keeping in mind that the remote is $20. A new Roku Stick+ is $50 (you can sometimes find them on sale for less). The 3500 was a good stick in its day, and while it's officially listed as "updatable," that model dates from 2014. The current sticks are noticeably faster. Keep that in mind when weighing the options.
The other drawback is that not all apps support the 3500 Stick. Peacock TV, for instance, doesn't support the device. You may find other modern apps dropping support for these older devices.
DBDukes https://www.dbdukes.com/Roku Ultra (4660) Roku Streambar (9102) Roku Streaming Stick+ (3810)
You can not buy a new remote for the 3500 purple stick, sorry recent wifi remote do not pair with the 3500 stick. You only remedy is to go used off of ebay. Roku 3 remotes pair with 3500, the headphone jack won't work but the volume keys will, unlike original 3500 remote.