Student train discounts in Germany without BahnCard?

I don't think there are any student-specific discounts, except that you can get the BahnCard about 1/3rd off. But as you say, the BahnCard is for people who travel frequently, not for single trips.

Other ways to save money:

• Book your ticket as early as possible - there are limited quotas of cheaper tickets available if you do so.
• Use the Quer-Durchs-Land ticket, to travel as far as you can on a single day for 44 EUR - but you can only use local trains. Up to 4 people can accompany you for 6 EUR each.
• The Schönes-Wochenende-Ticket works the same, but only on weekends, and it's valid for up to 5 people and costs 42 EUR.
• The Länder-Tickets work the same but are restricted to a single state, prices start at 22 EUR.

I would check bahn.ltur -- I remember I got a ticket from Berlin to Frankfurt for just 26 Euro (normally about 135 Euro I think). I looked up Berlin to Hamburg and it also gives me options for 26 Euro tickets. Do know, that you have to make that specific train that you bought the ticket for. The other problem is I don't think you can buy tickets very far in advance.

I also found this link and you can get from Warsaw to Berlin for 48 Euros.

Not exactly sure what your budget is though.

But specifically for student discounts, I'm not sure. I was just visiting Germany a few months back and I used that discount site.

Just one more tip: If you go for a cheaper solution, have a look also at the buses which offer great discounts http://www.eurolines.de/de/internationale-fernbusse/fahrplaene/buslinien-deutschland-polen/

There are no student discounts available for DB tickets — neither for school nor for university students. Everybody aged 14 or older is required to pay the adult fare, no exceptions.^[1]

However, I wouldn’t blatantly discard the option of a BahnCard. There is a so-called Probe BahnCard (trial BahnCard) which only costs €19 but gives you the full 25 % discount on any ticket (excluding the flatrate tickets such as Schönes Wochenende). It is valid for three months. Since it automatically turns into a subscription, you need to explicitly terminate the contract in time. Your tickets need only cost more than €76 for the Probe BahnCard to be worth it.

[1]: Okay, strictly speaking that was a lie. Special commuting tickets are available at discounted prices for school and university students (Schülerwochenkarte and Schülermonatskarte), but they can only be bought with a confirmation by the school/uni, a special card onto which you write your address and which is stamped at a station and only for the route from home to school. So not an option here.