The rear panel on Alto TS series cabs is a bit of a doddle to remove - just take all the screws out around the edges - they're all just normal posi ones. Now, be careful when lifting the amp plate out because there are cables running to the woofer & tweeter. Unplug the cables going to the speakers, noting which colours go where.
Getting at the fan is fairly straightforward. Locate the red & black cable the fan is powered from & unplug it from the amplifier module. Make a careful note of where it plugs into. Then you can undo four little screws to remove the amplifier from the plate it's mounted on.. and then you should be able to get at the fan unhindered. It's a 60mm 12 volt fan & just about any of the same dimensions will do (I'd buy one from RS components if I were you, not ebay!). If you have a 12 volt power supply you can test the fan on, try that to determine if it's the problem.
By the sounds of things, the fan not working is the most likely cause of your operator's woes.
As for my views on Alto cabs.. the TS1xx series were amazingly good value for money if you treated them right. The woofers didn't like mechanical shocks & they sure as heck don't stand up to people running the cab on the limiter for long. With an upgraded driver from Blue Aran they can sound pretty punchy but the downside is a woofer with a decent power capacity weighs a darn sight more than the original factory fitted one. For a budget cab (I bought my TS115A ages ago for £400 including stands - the pair!) they're amazing. But are they GOOD? Hmmmm not really.
I've kept my TS115As on as backup for my RCF HD12As - I sold my SRM450 mk1s on the day after the RCFs arrived. I'm planning to upgrade the woofers in the altos by the end of the year though, just so they can take a bit more POWAH