As @Ricky points out, showing truncated HMAC values won't help the attacker finding the secret key, compared to a similar situation where the HMAC values would not be truncated. This makes sense: the truncation only removes information.
However, the attacker is not ultimately after the secret key. What the attacker really wants is to make forgeries, i.e. compute some HMAC values that the computer will accept as its own. Finding out the secret key allows making forgeries, but the ability to make forgeries does not necessarily entail knowledge of the private key.
Fortunately, HMAC tends to behave like a PRF, so there are two known methods to make a forgery:
Perform a brute force enumeration of possible keys until the right one is found (one that matches a few known value+HMAC pairs). This attack is defeated by choosing the key is in space large enough to make the enumeration unrealistic (i.e. you generate a 128-bit key with a cryptographically strong PRNG).
Luck. The attacker sends a random sequence of bits as HMAC value and hopes that it will work. This attack is defeated by not truncating HMAC values to too small a length, and/or applying other mitigations such as allowing only one try and irrevocably rejecting devices that once showed even a single bogus HMAC value (as you do).
The "luck" attack works with probability 2-n, where n is the size (in bits) of your truncated HMAC output. I.e. with a 32-bit output, then a luck-based forgery has probability 1 in 4 billions or so to go undetected. This is the best that can be done with a 32-bit output, in all generality; that HMAC behaves as a PRF means that it is "optimal" in that respect. If you truncate to 8 bits, then the attack success probability is 1 in 256, which is probably too much for comfort. But this is your decision to make, based on your usage context.
Also (again as @Ricky points out), beware of replay attacks. A valid MAC, assuming that there was no forgery, only demonstrates to the computer that it saw and "approved" the message contents at some point -- but not that it was the last message that it saw. Old message-HMAC pairs can be sent again by a fake device. To defeat replay attacks, you must maintain some state on the computer (the computer must remember something about the device, e.g. a "message sequence number", that is part of the data over which the MAC is computed, and incremented for each message).