@Mariah Porter I've lived through some pretty serious basement flooding issues on one of my own rentals, so I definitely feel your pain--it's not a fun situation.
My natural reaction was also to wonder about the seller's disclosures, and whether I could bring a lawsuit against the sellers, but I pretty quickly realized this wasn't feasible or advisable (in my situation, it would have been almost impossible to prove the sellers were negligent or withholding a disclosure, and the legal fees would have been steep). ...but, I'm not a lawyer, so it may be worth asking a lawyer anyway...
I think your first priority here is to figure out what's causing the flooding, and fix that issue as soon as possible.
Most houses have a drain at the lowest part of the slab that's intended to collect water in event of a flood (for instance, if a broken pipe caused a flood)--I assume that that's what this pipe is? If you pour water into this pipe, does the water disappear, or does it immediately back up? (it should disappear--and if it doesn't, you may need to call a plumber).
Regardless, you'll want to start investigating what caused the flooding, and try to zero in on the cause BEFORE you start trying to make any fixes (such as digging a sump). When I experienced flooding problems, it was natural to want to try to jump right into fixing the issue, but I soon realized I was just shooting in the dark until I knew the cause of the flooding (for me, it turned out to be a ground water issue)
There are lots of questions you can ask to try to determine the cause of the flooding--for instance, was the entire carpet soaked evenly, or was it only soaked in a particular spot? (either can be a clue for where the water's coming from). You said the ground is very frozen now, but was there any rain or snow melt in the last week or two? (if so, then it could be ground water coming up from under the house--in which case, a sump (or multiple sumps) can fix the issue. Is there a water supply line, or a sewer main in the area of the flooding? (either could be a source of water). Are there any large culverts, drainage ditches, street drains etc. near the house? (all are sources of water). What is the age of the property, what is the foundation made from, and what's the condition of the foundation? (water could possibly seep through cracks in a foundation wall). Are the foundation walls exposed, and if so, can you see any cracks or signs of water dripping down a foundation wall? etc., etc., etc.
If the issue does seem to be ground water, don't be afraid to call in a hydrologist, who can help you better understand how to fix the problem. (I called in a hydrologist when I had flooding issues, and for a couple hundred bucks, he gave me info I used to fix the problem myself for about $3k--when it would have cost about $30-60k if I had relied on pros! So, he was definitely worth the fee).
And most importantly, try to stay positive--I found my flooding issues to be one of the more stressful things I've experienced as a real estate investor, but they usually CAN be fixed (once you discover the cause), and it is possible to bounce back (believe it or not--I was able to completely fix the flooding issue at my property, and it's now the highest-performing property in my portfolio, so it was worth the headache).
Let us know if you have questions--getting input from a lot of people can be useful as you try to figure out the source of the problem, and potential solutions.
Good luck out there!