if it works while plugged in but doesn't hold a charge, it's likely the battery has died. they don't last forever, and I'd guess your 1st gen iPod touch may be a couple years old now
it's not hard to replace the battery yourself.
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update:
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you can find Apple's policy and pricing to replace out of warranty iPod batteries [http://www.apple.com/support/ipod/service/battery|here].
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You can see that their charge for 1st Gen iPod touch battery replacement is: $149(8GB)/$199(16GB)/$249(32GB). so probably the price they told you is correct, assuming you have 8GB model. Of course it's cheaper to replace it yourself.
if it works while plugged in but doesn't hold a charge, it's likely the battery has died. they don't last forever, and I'd guess your 1st gen iPod touch may be a few years old now
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if it works while plugged in but doesn't hold a charge, it's likely the battery has died. they don't last forever, and I'd guess your 1st gen iPod touch may be a couple years old now
if it works while plugged in but doesn't hold a charge, it's likely the battery has died. they don't last forever, and I'd guess your 1st gen iPod touch may be a few years old now
it's not hard to replace the battery yourself.