My vacuum requires the 38528-027 belt, which seems to no longer be available, and I can't figure out the new part # for it.

This can be because you need to adjust the tension or probably the pulley is no longer aligned.
So find out if the shaft is no longer straight also if the belt requires tension.

Cost isn't the main factor to get a quality vacuum. There are plenty of vacuums in all price ranges that may work great the first year or two. Some expensive vacuums have problems and require lots of maintenance. Most vacuums in the hundred dollar price range are good for about a year. Bagless vacuums require a lot more maintenance than a bagged vacuum. Filters must be cleaned frequently to insure good airflow, and the filters and belts should be replaced at least once per year on most models. Filter replacement on bagged vacuums is not as critical because the dirt goes into the bag keeping the insides of the vacuum a lot cleaner which makes it last longer. Some vacuums, Hoover Windtunnel for example are available as a bagged or bagless model. The bagged models perform much longer than the bagless models for the average consumer, mainly because most people do not maintain their vacuums properly. There are a few really great vacuums in the two to three hundred dollar range that can work great for 10 years or more with nominal routine maintenance. The best place to find one is at a reputable vacuum store.

On some carpets you may need a vacuum that can adjust the height for thicker or longer carpets. If it worked ok on your carpets before it may need a new belt or brush roll.

DC07s have two drive belts that turn the brush bar - one connects the output of the motor to the clutch, the other connects the clutch to the brush bar.
You can check the latter simply by removing the sole plate and looking. Unfortunately the other belt is hidden under a plastic cover, so you cant see if it is okay or not without some dismantling. This cover is not easy to remove and requires a Torx driver to under the securing screws.
If, after removing the cover, the other belt is okay, then you have a faulty clutch. New clutches are available on eBay reasonably cheaply, but again good tools and DIY skills are required.
Have a look atwww.dysonmedic.com which has some excellent info on dismantling and repairing a DC 07, but unless you have access to such tools, and feel confident to tackle it, it's probably time to call Dyson or a Vacuum repairer.

DC07s have two drive belts that turn the brush bar - one connects the output of the motor to the clutch, the other connects the clutch to the brush bar.
You can check the latter simply by removing the sole plate and looking. Unfortunately the other belt is hidden under a plastic cover, so you cant see if it is okay or not without some dismantling. This cover is not easy to remove and requires a Torx driver to under the securing screws.
If, after removing the cover, the other belt is okay, then you have a faulty clutch. New clutches are available on eBay reasonably cheaply, but again good tools and DIY skills are required.
Have a look at www.dysonmedic.com which has some excellent info on dismantling and repairing a DC 07, but unless you have access to such tools, and feel confident to tackle it, it's probably time to call Dyson or a Vacuum repairer.

DC07s have two drive belts that turn the brush bar - one connects the output of the motor to the clutch, the other connects the clutch to the brush bar.
You can check the latter simply by removing the sole plate and looking. Unfortunately the other belt is hidden under a plastic cover, so you cant see if it is okay or not without some dismantling. This cover is not easy to remove and requires a Torx driver to under the securing screws.
If, after removing the cover, the other belt is okay, then you have a faulty clutch. New clutches are available on eBay reasonably cheaply, but again good tools and DIY skills are required.
Have a look at www.dysonmedic.com which has some excellent info on dismantling and repairing a DC 07, but unless you have access to such tools, and feel confident to tackle it, it's probably time to call Dyson or a Vacuum repairer.

DC7s have two drivebelts that turn the brush bar - one connects the output of the motor to the clutch, the other connects the clutch to the brush bar.
You can check the latter simply by removing the sole plate and looking. Unfortunately the other belt is hidden under a plastic cover, so you cant see if it is okay or not without some dismantling. This cover is not easy to remove and requires a Torx driver to under the securing screws.
If, after removing the cover, the other belt is okay, then you have a faulty clutch. New clutches are available on eBay reasonably cheaply, but again good tools and DIY skills are required.
Have a look at www.dysonmedic.com which has some excellent info on dismantling and repairing a DC 07, but unless you have access to such tools, and feel confident to tackle it, it's probably time to call Dyson or a Vacuum repairer.

Most likely your belt wore out and broke.
Here is a handy vacuum repair tutorial that should get you back cleaning.

Below is a short excerpt from the instructions. The link above will take you to the full version with images.
When your vacuum starts to lose cleaning power, requiring multiple passes to get an area clean, or the self-propulsion loses its zip, chances are you need to change the vacuum agitator belt. After only a few months of use, most vacuum belts stretch out enough to slip, causing the agitator to spin more slowly.
Replacing the belt is quick and inexpensive. New belts are available starting at about $5. Belts come in numerous brands and sizes, so bring the old one to the store for a guaranteed match.
Fifteen minutes, two screwdrivers and a new belt are all you’ll typically need to complete the job.

you probablly need a new belt clutch it should go to a vac shop it isnt an easy fix

good job