That's what I put and it was accepted. But "They can not check this?" is a question, because it has a question mark, and it would be said with a rising inflection.
It may not be the clearest way of phrasing a question, but in every day conversation English speakers do this all the time. I.e. They change the inflection.
They can be used interchangeably, but usually it's "cannot"
Also, the word order you have is incorrect. It should be: They cannot check this?
As someone who is not a scientist, checking and verifying is still part of my everyday life. Checking my child's homework would normally use revisar, but verifying that he has done his homework would be comprobar. You check/verify appointment times, addresses and phone numbers, and whether you have enough eggs to make a cake.
"Try" is different from "check" or "prove." In some circumstances, one might say, "can you try this to see if it works?"
But other times, I would say "check". "My car is running badly -- can you check it?" Probably not say:: "My car is running badly, can you try it."
According to SpanishDict.com, the primary meanings are: check, prove. Comprobar also = check, ascertain, test, prove, make sure, substantiate, etc. It helps to look at the many different meanings to understand the word.
"Ascertain" means "determine" . Similar to "check" but not the same, I suggest. Spanishdict.com says that "establecer" (establish) and "determinar" are words for "ascertain.".
SpaniDict also gives "averiguar" for "ascertain" , which according to RAE, comes from the Latin "verficar" (verify"
According to RAE, "comprobar" means "determine the veracity" or "accuracy of something."
"Comprobar" comes from the Latin "comprobare" which means "to test". Other meanings of the Latin "comprobare" are "prove, establish, attest, make good, approve, verify as true, etc."
I would think that "ascertain" should be accepted. I suggest that "check" may not be the best translation of "comprobar", and that "ascertain" would be better, FWIW
"Can't they..." = "Ellos no pueden..."
"Aren't they able to..." = "Ellos no son capaces de..."
It's important to understand that there is a difference between two things expressing the same idea, and being a translation. DL generally only accepts accurate translations, not sentences that just express the same idea.
p.s. The adjective used in the second phrase is "capaz", but the "z" changes to a "c" in the plural form (the same way that "pez" becomes "peces").