Can folks here recommend a reliable vacuum cleaner that will work for ten years without breaking down? Less than $100 preferably. New, not used. Have had bad luck with all brands/models we have tried in the past. Hopefully vacuums that last ten years do exist!
Something decent under $100 is difficult.
Shark vacuums are excellent and worth the price.
This one is decent - https://www.amazon.com/Navigator-Lift-Away-Anti-Allergy-NV352-Lavender/dp/B004Q4DRJW
It was $100 when I bought it but is $145 now.
Shark NV352 Navigator Lift-Away Upright Vacuum
$69.99 + shipping
Factory Reconditioned
https://www.woot.com/offers/shark-nv352-navigator-lift-away-upright-vacuum
I doubt you'll find one with a ten year warranty for under a 100 bucks.I have a Dirt Devil ultralite that I paid $ 50 for about 7 or 8 years ago, but I only vacuum about once a year. I kid you. Here are a couple inexpensive Hoover vacs.
Everything nowadays is designed to fail within a few years. Keeps the economy rolling. 
Refurbished: Shark UV540 Navigator Lift-Away Professional Upright Vacuum, Gray (Certified Refurbished)
$59.99 + Free Shipping
isn't it too much to expect longevity for a vacuum cleaner that comes under $100? vacuum cleaner last as high as 8 years based on the consumer reports. however life span might vary based on how you use, maintenance, and the brand that you purchased. checkout the best canister vacuum with retractable cord, if you are looking for the best vacuum cleaners in the market. however, Armor All AA255 Canister vacuum cleaner, Bissell 1332 Cleanview Rewind Upright, Hoover Linx Bagless SH20030 Vacuum are some of the Best Vacuum Cleaners Under $100 to Buy in 2020.
In fact canister vacuums are more expensive then just a few years ago with less features.
I used to buy hepa filter bagged canister kenmore vacuum. They were made by panasonic.
Then Kenmore (sears) replaced the cheaper (under $300) vacuums with a Chinese factory.
We found on amazon the same panasonic vacuum with only difference was the name on the vacuum. For $179 to $200
Should of bought 2 of them. Panasonic stopped making vacuums
Now the cheapest similar product starts at $300 to $400.
Even the Chinese factory is selling through mom and pop stores their Kenmore vacuum for $300.
So what can you get for $100???
$60 should look at the comments thread. I hope P. Quinn, who was the OP from 1 year and 7 months ago, purchased a vacuum and has vacuumed since his OP.
Shark Navigator Lift-Away UV540-RB Upright Vacuum - Bagless - HEPA
$59.99.
This upright vacuum features swivel steering for maneuvering around furniture and a detachable canister for portable cleaning ...
November 2018 · Shark · Navigator · Navigator Lift-Away · Upright · Bagless · HEPA Filter · 16 lb · For Pets · 0.3 gal
Other style options: Grey
Well unfortunately it is
Not:
Canister
New
Bagged (uses bags)
Hepa filter?
Consumer reports only has Miele as a high reliability cannister vacuum. They run about $1000.
Otherwise the cheapest cannister that they recommend is $220.
Shark are the highest reliability uprights and the cheapest recommended Shark is $170.
Otherwise there is a recommended Hoover for $130 which has slightly less reliability.
We have a Eureka vac that is 15 years old purchased for $150. Still working fine. Adjusted for inflation, that is $199 in today's money.
There is another way to get a reliable bagged vac with hepa for $100 (and sometimes quite a bit less as I was able to do with a bit of luck) but it won't work for everyone. I'll pm you.
Get rid of the carpets!
There was disgusting filth and mold under the carpets in the carpet padding when we renovated a fixer upper home we purchased.
The carpets appeared spotless, we just did not like the color.
Carpets | American Lung Association.