What is Reddit's opinion of AmScope SM-4TZ-144A Professional Trinocular Stereo Zoom Microscope, WH10x Eyepieces, 3.5X-90X Magnification, 0.7X-4.5X Zoom Objective, Four-Zone LED Ring Light, Double-Arm Boom Stand, 110V-240V, Includes 0.5X and 2.0X Barlow Lens?

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Its buggered/broken/knackered you're trying to troubleshoot something that should be e-waste.

Strip the cooler, replace Thermal paste. Check to see if any caps or resisters have fallen off or popped. Do a board level trace and power flow check with one of these:

https://www.amazon.co.uk/dp/B004UBNIMC?tag=clevercreatio-21&geniuslink=true

If not recycle time.

The head is an SMZ-2B. I'm not sure what the stand is.

I find having adjustable zoom is also very helpful. I think the ST4Z (maybe wrong numbers?) has that feature.

EDIT: This microscope is what I meant.

 

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This is the scope I have, with this camera. Within your budget, I think a zoom scope will be pretty difficult to manage; consider used scopes, but if you go that route make sure you go through a reputable dealer. Interchangeable objectives really aren't that big a deal, though, it just might get a little annoying with some specimens; it certainly beats no scope at all!

I bought this one at Christmas:

https://www.amazon.com/gp/product/B004UBNIMC/

I already own a Nikon YS (Picked up on Craigslist for $100) without the trinocular port, so I knew I wanted something that was lit from the top. You can probably get just the head:

https://www.amazon.com/AmScope-SM7180T-7X-180X-Trinocular-Microscope/dp/B005MKI5NW/

The Nikon allows me to see individual red blood cells moving around, the Amscope doesn't get that kind of magnification and the lighting is wrong. You can record video through holding the phone as well and I've done video of the red blood cells moving around.

Found it! https://www.youtube.com/watch?v=7rkeCcYyCVI